19-SimpleStructureSet/Seminar19.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Семинар 19\n",
    "# Оптимизация на множествах простой структуры"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## На прошлом семинаре...\n",
    "\n",
    "- История линейного программирования\n",
    "- Концепция методов внутренней точки\n",
    "- Прямой барьерный метод\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Методы решения каких задач уже известны\n",
    "\n",
    "- Безусловная минимизация: функция достаточно гладкая, но ограничений на аргумент нет.\n",
    "- Линейное программирование: линейная функция при линейных ограничениях\n",
    "\n",
    "Следующий шаг: произвольная достаточно гладкая функция на достаточно простом множестве - не обязательно полиэдральном."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Что такое \"простое множество\"?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Определение.** Множество будем называть *простым*, если проекцию на него можно найти существенно быстрее (чаще всего аналитически) по сравнению с решением исходной задачи минимизации."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Примеры простых множеств\n",
    "\n",
    "- Полиэдр $Ax = b, Cx \\leq d$\n",
    "    - аффинное множество\n",
    "    - гиперплоскость\n",
    "    - полупространство\n",
    "    - отрезок, интервал, полуинтервал\n",
    "    - симплекс\n",
    "- Конусы\n",
    "    - положительный ортант\n",
    "    - Лоренцев конус\n",
    "    - $\\mathbb{S}^n_{+}$\n",
    "    \n",
    "**Замечание:** убедитесь, что Вы понимаете, что стоит за этими названиями и обозначениями!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Напоминание: как искать проекцию?\n",
    "Для данной точки $y \\in \\mathbb{R}^n$ требуется решить следующую задачу\n",
    "$$\n",
    "\\min_{x \\in P} \\|x - y \\|_2\n",
    "$$\n",
    "Обозначение: $\\pi_P(y)$ - проекция точки $y$ на множество $P$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Примеры проекций\n",
    "\n",
    "- Отрезок $P = \\{x | l \\leq x \\leq u \\}$\n",
    "$$\n",
    "(\\pi_P(y))_k = \n",
    "\\begin{cases}\n",
    "u_k & y_k \\geq u_k \\\\\n",
    "l_k & y_k \\leq l_k \\\\\n",
    "y_k & \\text{otherwise.}\n",
    "\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Аффинное множество $P = \\{ x| Ax = b \\}$\n",
    "$$\n",
    "\\pi_P(y) = y - A^+(Ay - b),\n",
    "$$ \n",
    "где $A^+$ - псевдообратная матрица. Если $A$ полного ранга и столбцы линейно-независимы, тогда $A^+ = (A^{\\top}A)^{-1}A^{\\top}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- Конус положительно полуопределённых матриц $P = \\mathbb{S}^n_+ = \\{X \\in \\mathbb{R}^{n \\times n} | X \\succeq 0, \\; X^{\\top} = X \\}$\n",
    "$$\n",
    "\\pi_P(Y) = \\prod_{i=1}^n (\\lambda_i)_+ v_i v_i^{\\top},\n",
    "$$\n",
    "где $(\\lambda_i, v_i)$ - пары собственных значений и векторов матрицы $Y$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Метод проекции градиента"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\n",
    "\\min_{x \\in P} f(x)\n",
    "$$\n",
    "**Идея**: делать шаг градиентного спуска и проецировать полученную точку на допустимое множество $P$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Псевдокод\n",
    "\n",
    "```python\n",
    "def ProjectedGradientDescent(f, gradf, proj, x0, tol):\n",
    "    x = x0\n",
    "    while True:\n",
    "        gradient = gradf(x)\n",
    "        alpha = get_step_size(x, f, gradf, proj)\n",
    "        x = proj(x - alpha * grad)\n",
    "        if check_convergence(x, f, tol):\n",
    "            break\n",
    "    return x\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Поиск шага\n",
    "\n",
    "- Постоянный шаг: $\\alpha_k = \\alpha$, где $\\alpha$ достаточно мало\n",
    "- Наискорейший спуск: \n",
    "$$\n",
    "\\min_{\\alpha > 0} f(x_k(\\alpha))\n",
    "$$\n",
    "$x_k(\\alpha) = \\pi_P (x_k - \\alpha f'(x_k))$\n",
    "- Линейный поиск: уменьшать шаг по правилу Армихо, пока не будет выполнено условие\n",
    "$$\n",
    "f(x_k(\\alpha)) - f(x_k) \\leq c_1 \\langle f'(x_k), x_k(\\alpha) - x_k \\rangle\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Теорема сходимости (Б.Т. Поляк \"Введение в оптимизацию\", гл. 7, $\\S$ 2)\n",
    "\n",
    "**Теорема.** Пусть $f$ выпуклая дифференцируемая функция и её градиент липшицев на $P$ с константой $L$. Пусть $P$ выпуклое и замкнутое множество и $0 < \\alpha < 2 / L$. \n",
    "\n",
    "Тогда\n",
    "- $x_k \\to x^*$\n",
    "- если $f$ сильно выпуклая, то $x_k \\to x^*$ со скоростью геометрической прогрессии\n",
    "- если $f$ дважды дифференцируема и $f''(x) \\succeq l\\mathbf{I}, \\; x \\in P$, $l > 0$, то знаменатель прогрессии $q = \\max \\{ |1 - \\alpha l|, |1 - \\alpha L|\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Критерии остановки\n",
    "- Сходимость по аргументу, то есть сходимость последовательности $x_k$ к предельной точке $x^*$\n",
    "- $x_k = x^*$ если $x_k = \\pi_P(x_{k+1})$\n",
    "\n",
    "**Важное замечание:** проверять норму градиента бессмысленно, так как это условная оптимизация!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Аффинная инвариантность\n",
    "\n",
    "**Упражнение.** Проверьте является ли метод проекции градиента аффинно инвариантным."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Pro & Contra\n",
    "\n",
    "Pro\n",
    "- часто можно аналитически вычислить проекцию\n",
    "- сходимость аналогична градиентному спуску в безусловной оптимизации\n",
    "- обобщается на негладкий случай - метод проекции субградиента\n",
    "\n",
    "Contra\n",
    "- при больших $n$ аналитическое вычисление проекции может быть слишком затратно: $O(n)$ для симплекса vs. решение задачи квадратичного программирования для полиэдрального множества\n",
    "- при обновлении градиента может теряться структура задачи: разреженность, малоранговость..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Что такое \"простое множество\"?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Определение.** Множество $D$ будем называть *простым*, если можно найти решение следующей задачи\n",
    "$$\n",
    "\\min_{x \\in D} c^{\\top}x\n",
    "$$\n",
    "существенно быстрее (чаще всего аналитически) по сравнению с решением исходной задачи минимизации."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Примеры простых множеств\n",
    "\n",
    "- Полиэдральное множество - задача линейного программирования вместо квадратичного программирования\n",
    "- Симплекс - $x^* = e_i$, где $c_i = \\max\\limits_{k = 1,\\ldots, n} c_k$\n",
    "- Лоренцев конус - $x^* = -\\frac{ct}{\\| c\\|_2}$\n",
    "- Все остальные множества из предыдущего определения\n",
    "\n",
    "**Замечание 1:** отличие этого определения от предыдущего в линейности целевой функции (была квадратичная), поэтому простых множеств для этого определения больше.\n",
    "\n",
    "**Замечание 2:** иногда на допустимое множество легко найти проекцию, но задача линейного программирования является неограниченной. Например, для множества \n",
    "$$\n",
    "D = \\{ x \\in \\mathbb{R}^n \\; | \\; x_i \\geq 0 \\},\n",
    "$$ \n",
    "проекция на которое очевидна, решение задачи линейного программирования равно $-\\infty$, если есть хотя бы одна отрицательная компонента вектора $c$. Теорема с объяснением будет ниже."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Метод условного градиента <br> (aka Frank-Wolfe algorithm (1956))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\n",
    "\\min_{x \\in D} f(x)\n",
    "$$\n",
    "\n",
    "**Идея**: делать шаг не по градиенту, а по направлению, которое точно не выведет из допустимого множества.\n",
    "\n",
    "Аналогия с градиентным спуском: линейная аппроксимация **на допустимом множестве**:\n",
    "$$\n",
    "f(x_k + s_k) = f(x_k) + \\langle f'(x_k), s_k \\rangle \\to \\min_{{\\color{red}{s_k \\in D}}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Условный градиент\n",
    "\n",
    "**Определение** Направление $s_k - x_k$ называют *условным градиентом* функции $f$ в точке $x_k$ на допустимом множестве $D$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Псевдокод\n",
    "```python\n",
    "def FrankWolfe(f, gradf, linprogsolver, x0, tol):\n",
    "    x = x0\n",
    "    while True:\n",
    "        gradient = gradf(x)\n",
    "        s = linprogsolver(gradient)\n",
    "        alpha = get_step_size(s, x, f)\n",
    "        x = x + alpha * (s - x)\n",
    "        if check_convergence(x, f, tol):\n",
    "            break\n",
    "    return x\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Выбор шага\n",
    "\n",
    "- Постоянный шаг: $\\alpha_k = \\alpha$\n",
    "- Убывающая последовательность, стандартный выбор $\\alpha_k = \\frac{2}{k + 2}$\n",
    "- Наискорейший спуск:\n",
    "$$\n",
    "\\min_{{\\color{red}{0 \\leq \\alpha_k \\leq 1}}} f(x_k + \\alpha_k(s_k - x_k))\n",
    "$$\n",
    "- Линейный поиск по правилу Армихо: должно выполняться условие\n",
    "$$\n",
    "f((x_k + \\alpha_k(s_k - x_k)) \\leq f(x_k) + c_1 \\alpha_k \\langle f'(x_k), s_k - x_k \\rangle\n",
    "$$\n",
    "Начинать поиск нужно с $\\alpha_k = 1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Критерий остановки\n",
    "\n",
    "- Так как показана сходимость к предельной точке $x^*$, то критерием остановки является сходимость по аргументу\n",
    "- Если $f(x)$ выпукла, то $f(s) \\geq f(x_k) + \\langle f'(x_k), s - x_k \\rangle$ для любого вектора $s$, а значит и для любого $s \\in D$. Следовательно\n",
    "\n",
    "$$\n",
    "f(x^*) \\geq f(x) + \\min_{s \\in D} \\langle f'(x), s - x\\rangle\n",
    "$$\n",
    "\n",
    "или\n",
    " \n",
    "$$\n",
    "f(x) - f(x^*) \\leq -\\min_{s \\in D} \\langle f'(x), s - x\\rangle = \\max_{s \\in D} \\langle f'(x), x - s\\rangle = g(x)\n",
    "$$\n",
    "Получили аналог зазора двойственности для контроля точности и устойчивости решения."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Аффинная инвариантность\n",
    "\n",
    "- Метод условного градиента является аффинно инвариантным относительно сюръективных отображений\n",
    "- Скорость сходимости и вид итерации не меняется"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Теорема сходимости (лекции)\n",
    "\n",
    "**Теорема 4.2.1.** Пусть $X$ - **выпуклый компакт** и $f(x)$ - дифференцируемая функция на $X$ с Липшицевым градиентом. Шаг выбирается по правилу Армихо. Тогда **для любого ${\\color{red}{x_0 \\in X}}$ **\n",
    "- метод условного градиента генерирует последовательность $\\{x_k\\}$, которая имеет предельные точки\n",
    "- любая предельная точка $x^*$ является **стационарной**\n",
    "- если $f(x)$ выпукла на $X$, то $x^*$ - решение задачи"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Теоремы сходимости\n",
    "\n",
    "**Теорема (прямая).([Convex Optimization: Algorithms and Complexity, Th 3.8.](https://arxiv.org/abs/1405.4980))** Пусть $f$ выпуклая и дифференцируемая функция и её градиент Липшицев с константой $L$. Множество $X$ - выпуклый компакт диаметра $d > 0$. \n",
    "Тогда метод условного градиента с шагом $\\alpha_k = \\frac{2}{k + 1}$ сходится как\n",
    "$$\n",
    "f(x^*) - f(x_k) \\leq \\dfrac{2d^2L}{k + 2}, \\quad k \\geq 1\n",
    "$$\n",
    "\n",
    "**Теорема (двойственная) [см. эту статью](http://m8j.net/math/revisited-FW.pdf).** После выполнения $K$ итераций метода условного градиента для выпуклой и непрерывно дифференцируемой функции для функции $g$ и любого $k \\leq K$ выполнено\n",
    "$$\n",
    "g(x_k) \\leq \\frac{2\\beta C_f}{K+2} (1 + \\delta),\n",
    "$$\n",
    "где $\\beta \\approx 3$, $\\delta$ - точность решения промежуточных задач, $C_f$ - оценка кривизны $f$ на множестве $D$\n",
    "$$\n",
    "C_f = \\sup_{x, s \\in D; \\gamma \\in [0,1]} \\frac{2}{\\gamma^2}\\left(f(x + \\gamma(s - x)) - f(x) - \\langle \\gamma(s - x), f'(x)\\rangle\\right)\n",
    "$$\n",
    "\n",
    "Аргумент супремума так же известен как *дивергенция Брегмана*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Как конструткивно задать \"простые\" множества?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Определение**. Atomic norm называется следующая функция \n",
    "\n",
    "$$\n",
    "\\|x\\|_{\\mathcal{D}} = \\inf_{t \\geq 0} \\{ t | x \\in t\\mathcal{D} \\}\n",
    "$$\n",
    "\n",
    "Она является нормой если симметрична и $0 \\in \\mathrm{int}(\\mathcal{D})$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Сопряжённая atomic norm\n",
    "$$\n",
    "\\|y\\|^*_{\\mathcal{D}} = \\sup_{s \\in \\mathrm{D}} \\langle s, y \\rangle\n",
    "$$\n",
    "\n",
    "- Из определения выпуклой оболочки следует, что линейная функция достигает максимума в одной из \"вершин\" выпуклого множества\n",
    "- Следовательно, $\\| y \\|^*_{\\mathcal{D}} = \\| y \\|^*_{\\mathrm{conv}(\\mathcal{D})}$\n",
    "- Это позволяет эффективно вычислять решение промежуточных задач для опредлеения $s$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"atomic_table.png\">\n",
    "Таблица взята из [статьи](http://m8j.net/math/revisited-FW.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Разреженность vs. точность\n",
    "\n",
    "- Метод условного градиента на каждой итерации добьавляет к решению слагаемое, являющееся элементом множества $\\mathcal{A}$\n",
    "- Решение моджет быть представлено в виде комбинации элементов $\\mathcal{A}$\n",
    "- Теорема Каратеодори\n",
    "- Число элементов может быть существенно маньше требуемого теоремой Каратеодори"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Эксперименты"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Пример 1\n",
    "\n",
    "\\begin{equation*}\n",
    "\\begin{split}\n",
    "& \\min \\|Ax - b \\|_2\\\\\n",
    "\\text{s.t. } & 0 \\leq x_i \\leq 1\n",
    "\\end{split}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def f(x, p):\n",
    "    return 0.5 * np.linalg.norm(p[\"A\"].dot(x) - p[\"b\"])**2\n",
    "\n",
    "def grad_f(x, p):\n",
    "    grad = -p[\"A\"].T.dot(p[\"b\"])\n",
    "    grad = grad + p[\"A\"].T.dot(p[\"A\"].dot(x))\n",
    "    return grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def linsolver(gradient):\n",
    "    x = np.zeros(gradient.shape[0])\n",
    "    pos_grad = gradient > 0\n",
    "    neg_grad = gradient < 0\n",
    "    x[pos_grad] = np.zeros(np.sum(pos_grad == True))\n",
    "    x[neg_grad] = np.ones(np.sum(neg_grad == True))\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def projection(y):\n",
    "    return np.clip(y, 0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import ssopt\n",
    "import numpy as np\n",
    "\n",
    "n = 50\n",
    "m = 100\n",
    "A = np.random.randn(m, n)\n",
    "x_true = np.random.rand(n)\n",
    "b = A.dot(x_true) + 0.01 * np.random.randn(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def myplot(x, y, xlab, ylab, xscale=\"linear\", yscale=\"log\"):\n",
    "    plt.figure(figsize=(10, 8))\n",
    "    plt.xscale(xscale)\n",
    "    plt.yscale(yscale)\n",
    "    for key in y:\n",
    "        plt.plot(x[key], y[key], label=key)\n",
    "    plt.xticks(fontsize=18)\n",
    "    plt.yticks(fontsize=18)\n",
    "    plt.legend(loc=\"best\", fontsize=24)\n",
    "    plt.xlabel(xlab, fontsize=24)\n",
    "    plt.ylabel(ylab, fontsize=24)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max iterations = 200 exceeds\n",
      "Diff function on last iteration = 0.002803342655863905\n",
      "Norm diff x on last iteration = 0.0030579239492299357\n",
      "f* = 0.7504095060569309\n",
      "Optimal value CG = 0.7504095060569309\n",
      "Time for CG = 0.05517697334289551 sec.\n"
     ]
    }
   ],
   "source": [
    "x0 = np.random.rand(n)\n",
    "cg = ssopt.CondGD(maxiter=200, tol=1e-10)\n",
    "hist_cg = []\n",
    "def callback_cg(x):\n",
    "    hist_cg.append(x)\n",
    "res = cg.solve(f, grad_f, linsolver, x0, {\"A\": A, \"b\": b, \"callback\": callback_cg, \"disp\": 0})\n",
    "x_cg = res[\"x\"]\n",
    "time_cg = res[\"time\"]\n",
    "print(\"Optimal value CG =\", f(x_cg, {\"A\": A, \"b\": b}))\n",
    "print(\"Time for CG =\", time_cg, \"sec.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tolerance reached on iteration 128\n",
      "Diff function = 9.18037165384411e-11\n",
      "Norm diff x = 3.035227084523093e-06\n",
      "f* = 0.0028364747953050374\n",
      "Optimal value PG = 0.0028364747953050374\n",
      "Time for PG = 0.0621640682220459 sec.\n"
     ]
    }
   ],
   "source": [
    "pg = ssopt.ProjGD(maxiter=200, tol=1e-10)\n",
    "hist_pg = []\n",
    "def callback_pg(x):\n",
    "    hist_pg.append(x)\n",
    "res = pg.solve(f, grad_f, projection, x0, {\"A\": A, \"b\": b, \"callback\": callback_pg, \"disp\": 0})\n",
    "x_pg = res[\"x\"]\n",
    "time_pg = res[\"time\"]\n",
    "print(\"Optimal value PG =\", f(x_pg, {\"A\": A, \"b\": b}))\n",
    "print(\"Time for PG =\", time_pg, \"sec.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113f7ee48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rc(\"text\", usetex=True)\n",
    "y_hist_f_cg = [f(x, {\"A\": A, \"b\": b}) for x in hist_cg]\n",
    "y_hist_f_pg = [f(x, {\"A\": A, \"b\": b}) for x in hist_pg]\n",
    "myplot({\"CG\": range(1, len(y_hist_f_cg) + 1), \"PG\": range(1, len(y_hist_f_pg) + 1)},\n",
    "       {\"CG\": y_hist_f_cg, \"PG\": y_hist_f_pg}, \"Number of iteration\",\n",
    "       r\"Objective function, $\\frac{1}{2}\\|Ax - b\\|^2_2$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CVX optimal value = 0.002836474314205269\n"
     ]
    }
   ],
   "source": [
    "import cvxpy as cvx\n",
    "\n",
    "x = cvx.Variable(n)\n",
    "obj = cvx.Minimize(0.5 * cvx.norm(A * x - b, 2)**2)\n",
    "# constr = [cvx.norm(x, 1) <= 1, x >= 0]\n",
    "constr = [x >= 0, x <= 1]\n",
    "problem = cvx.Problem(objective=obj, constraints=constr)\n",
    "value = problem.solve()\n",
    "x_cvx = np.array(x.value).ravel()\n",
    "print(\"CVX optimal value =\", value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Зависимость времени и числа итераций от точности"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tolerance reached on iteration 13\n",
      "Diff function = 0.8551045355275235\n",
      "Norm diff x = 0.043080264570766455\n",
      "f* = 9.046101378225186\n",
      "Tolerance reached on iteration 31\n",
      "Diff function = 0.06833025998989894\n",
      "Norm diff x = 0.012200296494396657\n",
      "f* = 3.172102528218107\n",
      "Tolerance reached on iteration 80\n",
      "Diff function = 0.006184319750470291\n",
      "Norm diff x = 0.0031712567537986254\n",
      "f* = 1.3917508978879582\n",
      "Tolerance reached on iteration 298\n",
      "Diff function = 0.0009733124425673756\n",
      "Norm diff x = 0.0015583286591963476\n",
      "f* = 0.5730929568309945\n",
      "Tolerance reached on iteration 928\n",
      "Diff function = 9.919673663000284e-05\n",
      "Norm diff x = 0.0004397710584108256\n",
      "f* = 0.305081304971536\n",
      "Tolerance reached on iteration 4349\n",
      "Diff function = 9.33122309862422e-06\n",
      "Norm diff x = 0.00011755492817255278\n",
      "f* = 0.10177272234878992\n",
      "Tolerance reached on iteration 16052\n",
      "Diff function = 6.618163378990793e-07\n",
      "Norm diff x = 2.8894530611062824e-05\n",
      "f* = 0.03228956171879414\n",
      "Tolerance reached on iteration 53606\n",
      "Diff function = 9.981110554203865e-08\n",
      "Norm diff x = 1.3062927057481504e-05\n",
      "f* = 0.013251175581999456\n"
     ]
    }
   ],
   "source": [
    "eps = [10**(-i) for i in range(8)]\n",
    "time_pg = np.zeros(len(eps))\n",
    "time_cg = np.zeros(len(eps))\n",
    "iter_pg = np.zeros(len(eps))\n",
    "iter_cg = np.zeros(len(eps))\n",
    "for i, tol in enumerate(eps):\n",
    "    pg = ssopt.ProjGD(maxiter=None, tol=tol)\n",
    "    res = pg.solve(f, grad_f, projection, x0, {\"A\": A, \"b\": b, \"disp\": -1})\n",
    "    time_pg[i] = res[\"time\"]\n",
    "    iter_pg[i] = res[\"num_iter\"]\n",
    "    cg = ssopt.CondGD(maxiter=None, tol=tol)\n",
    "    res = cg.solve(f, grad_f, linsolver, x0, {\"A\": A, \"b\": b, \"disp\": 0})\n",
    "    time_cg[i] = res[\"time\"]\n",
    "    iter_cg[i] = res[\"num_iter\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181a109978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "myplot({\"CG\":eps, \"PG\": eps}, {\"CG\": time_cg, \"PG\": time_pg}, r\"Accuracy, $\\varepsilon$\", \"Time, s\", xscale=\"log\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181a3347f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "myplot({\"CG\":eps, \"PG\": eps}, {\"CG\": iter_cg, \"PG\": iter_pg}, r\"Accuracy, $\\varepsilon$\", \"Number of iteration\", xscale=\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Пример 2\n",
    "Пусть $A$ - пятидиагональная матрица. Рассмотрим задачу: \n",
    "\\begin{equation*}\n",
    "\\begin{split}\n",
    "& \\min \\frac{1}{2}x^{\\top}Ax \\\\\n",
    "\\text{s.t. } & \\| x\\|_1 \\leq 1 \\\\\n",
    "& x_i \\geq 0\n",
    "\\end{split}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def f(x, p):\n",
    "    return 0.5 * x.dot(p[\"A\"].dot(x))\n",
    "\n",
    "def grad_f(x, p):\n",
    "    return p[\"A\"].dot(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def linsolver(gradient):\n",
    "    x = np.zeros(gradient.shape[0])\n",
    "    idx_min = np.argmin(gradient)\n",
    "    if gradient[idx_min] > 0:\n",
    "        x[idx_min] = 0\n",
    "    else:\n",
    "        x[idx_min] = 1\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def projection(y):\n",
    "    x = y.copy()\n",
    "    if np.all(x >= 0) and np.sum(x) <= 1:\n",
    "        return x\n",
    "    x = np.clip(x, 0, np.max(x))\n",
    "    if np.sum(x) <= 1:\n",
    "        return x\n",
    "    n = x.shape[0]\n",
    "    bget = False\n",
    "    x.sort()\n",
    "    x = x[::-1]\n",
    "    temp_sum = 0\n",
    "    t_hat = 0\n",
    "    for i in range(n - 1):\n",
    "        temp_sum += x[i]\n",
    "        t_hat = (temp_sum - 1.0) / (i + 1)\n",
    "        if t_hat >= x[i + 1]:\n",
    "            bget = True\n",
    "            break\n",
    "    if not bget:\n",
    "        t_hat = (temp_sum + x[n - 1] - 1.0) / n\n",
    "    return np.maximum(y - t_hat, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x181a1c0390>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181a321f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.sparse as scsp\n",
    "\n",
    "n = 100\n",
    "main_diag = np.random.randn(n)\n",
    "subdiag = np.random.rand(n - 1)\n",
    "sub2diag = np.random.rand(n - 2)\n",
    "A = scsp.diags([sub2diag, subdiag, main_diag, subdiag, sub2diag], [-2, -1, 0, 1, 2])\n",
    "A = A + 100 * scsp.eye(n)\n",
    "plt.spy(A, markersize=0.5)\n",
    "# print(scsp.linalg.eigs(A, k=n-2)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tolerance reached on iteration 39\n",
      "Diff function = 9.570964309764265e-11\n",
      "Norm diff x = 5.193246483571559e-07\n",
      "f* = 1.2305525541125486e-10\n",
      "Optimal value CG = 1.2305525541125486e-10\n",
      "Time for CG = 0.005919933319091797 sec.\n"
     ]
    }
   ],
   "source": [
    "x0 = np.random.rand(n)\n",
    "x0 = x0 / x0.sum()\n",
    "cg = ssopt.CondGD(maxiter=200, tol=1e-10)\n",
    "hist_cg = []\n",
    "def callback_cg(x):\n",
    "    hist_cg.append(x)\n",
    "res = cg.solve(f, grad_f, linsolver, x0, {\"A\": A, \"b\": b, \"callback\": callback_cg, \"disp\": 0})\n",
    "x_cg = res[\"x\"]\n",
    "time_cg = res[\"time\"]\n",
    "print(\"Optimal value CG =\", f(x_cg, {\"A\": A, \"b\": b}))\n",
    "print(\"Time for CG =\", time_cg, \"sec.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tolerance reached on iteration 3\n",
      "Diff function = 0.0\n",
      "Norm diff x = 0.0\n",
      "f* = 0.0\n",
      "Optimal value PG = 0.0\n",
      "Time for PG = 0.007942914962768555 sec.\n"
     ]
    }
   ],
   "source": [
    "pg = ssopt.ProjGD(maxiter=200, tol=1e-10)\n",
    "hist_pg = []\n",
    "def callback_pg(x):\n",
    "    hist_pg.append(x)\n",
    "res = pg.solve(f, grad_f, projection, x0, {\"A\": A, \"b\": b, \"callback\": callback_pg, \"disp\": 0})\n",
    "x_pg = res[\"x\"]\n",
    "time_pg = res[\"time\"]\n",
    "print(\"Optimal value PG =\", f(x_pg, {\"A\": A, \"b\": b}))\n",
    "print(\"Time for PG =\", time_pg, \"sec.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181a20aa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_hist_f_cg = [f(x, {\"A\": A, \"b\": b}) for x in hist_cg]\n",
    "y_hist_f_pg = [f(x, {\"A\": A, \"b\": b}) for x in hist_pg]\n",
    "myplot({\"CG\": range(1, len(y_hist_f_cg) + 1), \"PG\": range(1, len(y_hist_f_pg) + 1)},\n",
    "       {\"CG\": y_hist_f_cg, \"PG\": y_hist_f_pg}, \"Number of iteration\", r\"Objective function\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Зависимость времени и числа итераций от точности"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "eps = [10**(-i) for i in range(8)]\n",
    "time_pg = np.zeros(len(eps))\n",
    "time_cg = np.zeros(len(eps))\n",
    "iter_pg = np.zeros(len(eps))\n",
    "iter_cg = np.zeros(len(eps))\n",
    "for i, tol in enumerate(eps):\n",
    "    pg = ssopt.ProjGD(maxiter=None, tol=tol)\n",
    "    res = pg.solve(f, grad_f, projection, x0, {\"A\": A, \"b\": b, \"disp\": -1})\n",
    "    time_pg[i] = res[\"time\"]\n",
    "    iter_pg[i] = res[\"num_iter\"]\n",
    "    cg = ssopt.CondGD(maxiter=None, tol=tol)\n",
    "    res = cg.solve(f, grad_f, linsolver, x0, {\"A\": A, \"b\": b, \"disp\": -1})\n",
    "    time_cg[i] = res[\"time\"]\n",
    "    iter_cg[i] = res[\"num_iter\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x181a2989b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "myplot({\"CG\":eps, \"PG\": eps}, {\"CG\": time_cg, \"PG\": time_pg}, \n",
    "       r\"Accuracy, $\\varepsilon$\", \"Time, s\", xscale=\"log\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1151441d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "myplot({\"CG\":eps, \"PG\": eps}, {\"CG\": iter_cg, \"PG\": iter_pg},\n",
    "       r\"Accuracy, $\\varepsilon$\", \"Number of iteration\", xscale=\"log\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CVX optimal value = -5.450106669582896e-09\n"
     ]
    }
   ],
   "source": [
    "x = cvx.Variable(n)\n",
    "obj = cvx.Minimize(cvx.quad_form(x, A))\n",
    "constr = [cvx.norm(x, 1) <= 1, x >= 0]\n",
    "problem = cvx.Problem(objective=obj, constraints=constr)\n",
    "value = problem.solve()\n",
    "x_cvx = np.array(x.value).ravel()\n",
    "print(\"CVX optimal value =\", value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Pro & Contra\n",
    "\n",
    "Pro\n",
    "- Оценка сходимости для функционала **не зависит** от размерности\n",
    "- Если множество - многоугольник, то $x_k$ - выпуклая комбинация $k$ вершин многоугольника - разреженная решение для $k \\ll n$\n",
    "- Если множество выпуклая комбинация некоторых элементов, то решение - линейная комбинация подмножества этих элементов\n",
    "- Сходимость по функционалу не улучшаема даже для сильно выпуклых функций\n",
    "- Упрощение понятия \"простое множество\"\n",
    "- Существует подобие зазора двойственности и теоретические результаты о сходимости\n",
    "\n",
    "Contra\n",
    "- Сходимость по функционалу только сублинейная вида $\\frac{C}{k}$\n",
    "- Не обобщается на негладкие задачи"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Резюме\n",
    "- Множество простой структуры\n",
    "- Проекция\n",
    "- Метод проекции градиента\n",
    "- Метод условного градиента"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3 (cvxpy)",
   "language": "python",
   "name": "cvxpy"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}