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.buildinfo

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+# Sphinx build info version 1
+# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: c62f1f10c075fad023e7e3bc3c7c21bb
+tags: 645f666f9bcd5a90fca523b33c5a78b7

_sources/api/index.rst.txt

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+.. _api:
+
+API
+===
+
+.. toctree::
+    :maxdepth: 2
+    :glob:
+
+    modeling/index
+    optimizers/index
+    problems/index

_sources/api/modeling/Annotation.rst.txt

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+Annotation
+==========
+
+.. doxygenclass:: idol::Annotation

_sources/api/modeling/Column.rst.txt

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+.. _api_Column:
+
+Column
+======
+
+.. doxygenclass:: idol::Column

_sources/api/modeling/Constant.rst.txt

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+.. _api_Constant:
+
+Constant
+========
+
+.. doxygenclass:: idol::Constant

_sources/api/modeling/Ctr.rst.txt

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+.. _api_Ctr:
+
+Ctr
+===
+
+.. doxygenclass:: idol::Ctr

_sources/api/modeling/Env.rst.txt

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+Env
+===
+
+.. doxygenclass:: idol::Env

_sources/api/modeling/Expr.rst.txt

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+.. _api_Expr:
+
+Expr
+====
+
+.. doxygenclass:: idol::Expr

_sources/api/modeling/LinExpr.rst.txt

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+LinExpr
+=======
+
+This class is used to represent linear expressions in the modeling interface of idol.
+
+It consists in a set of linear terms which represent products of keys (typically, variables) and scalars.
+
+.. admonition:: Example
+
+    In this example, we create a linear expression representing the following linear expression.
+
+    .. math::
+
+        3 x_0 + 2 x_1
+
+    .. code-block:: cpp
+
+        auto x = model.add_vars(Dim<1>(2), 0, Inf, Continuous, "x");
+
+        LinExpr lin_expr = 3 * x[0] + 2 * x[1];
+
+.. doxygenclass:: idol::LinExpr

_sources/api/modeling/Model.rst.txt

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+.. _api_model:
+
+Model
+=====
+
+The Model class is probably the most central of idol. It is used to represent a mathematical optimization problem of the
+following general form.
+
+.. math::
+
+    \begin{array}{lll}
+        \textrm{minimize } & \displaystyle \sum_{j=1}^n a_{0j}x_j + \sum_{j=1}^n\sum_{k=1}^n q_{jk}^0x_jx_k + b_0\\
+        \textrm{subject to } & \displaystyle \sum_{j=1}^n a_{ij}x_j + \sum_{j=1}^n\sum_{k=1}^n q^i_{jk}x_jx_k \le b_i & i=1,...,m \\
+        & l_j \le x_j \le u_j & j=1,...,m \\
+        & x_j\in\mathbb Z & j\in J_I,
+    \end{array}
+
+Here, :math:`x_1, ..., x_n` are the decision variables with bounds :math:`[l_1,u_1],...,[l_n,u_n]` (possibly,
+:math:`l_j = -\infty` or :math:`u_j = +\infty`). Note that some variables have integrality requirements (i.e., those whose
+indices are in :math:`J_I`). Other entities are input parameters of the problem and must typically have real values
+(e.g., :math:`c_j, a_{ij}, q_{jk}^i` and :math:`b_i\in\mathbb R`). Alternatively, optimization problems can also be maximization
+problems.
+
+.. admonition:: Example:
+
+    Here is a short example which builds and solves the following optimization problem.
+
+    .. math::
+
+        \begin{array}{ll}
+            \textrm{minimize } & -x_0 - 1.5 x_1 + 3 \\
+            \textrm{subject to } & x_0 + 2 x_1 \le 1.5 \\
+            & 0 \le x_0 \le 1 \\
+            & 0 \le x_1 \le 1
+        \end{array}
+
+    .. code-block:: cpp
+
+        Env env;
+
+        Model model(env);
+
+        auto x = model.add_vars(Dim<1>(2), 0, 1, Continuous, "x");
+
+        auto c = model.add_ctr(x[0] + 2 * x[1] <= 1.5);
+
+        model.set_obj_expr(-x[0] - 1.5 * x[1] + 3);
+
+        model.use(Gurobi());
+
+        model.optimize();
+
+        std::cout << "Best obj = " << model.get_best_obj() << std::endl;
+
+.. doxygenclass:: idol::Model

_sources/api/modeling/Param.rst.txt

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+.. _api_Param:
+
+Param
+=====
+
+.. doxygenclass:: idol::Param

_sources/api/modeling/QuadExpr.rst.txt

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+QuadExpr
+========
+
+.. doxygenclass:: idol::QuadExpr

_sources/api/modeling/Row.rst.txt

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+.. _api_Row:
+
+Row
+===
+
+.. doxygenclass:: idol::Row

_sources/api/modeling/SolutionDual.rst.txt

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+.. _api_SolutionDual:
+
+Solution::Dual
+================
+
+.. doxygenclass:: idol::Solution::Dual

_sources/api/modeling/SolutionPrimal.rst.txt

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+.. _api_SolutionPrimal:
+
+Solution::Primal
+================
+
+.. doxygenclass:: idol::Solution::Primal

_sources/api/modeling/TempCtr.rst.txt

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+.. _api_TempCtr:
+
+TempCtr
+=======
+
+.. doxygenclass:: idol::TempCtr

_sources/api/modeling/TempVar.rst.txt

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+.. _api_TempVar:
+
+TempVar
+=======
+
+.. doxygenclass:: idol::TempVar

_sources/api/modeling/Var.rst.txt

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+.. _api_var:
+
+Var
+===
+
+.. doxygenclass:: idol::Var

_sources/api/modeling/index.rst.txt

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+.. _api_modeling:
+
+Modeling
+========
+
+.. toctree::
+    :maxdepth: 1
+    :glob:
+
+    *

_sources/api/optimizers/branch-and-bound/BranchAndBound.rst.txt

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+.. _api_BranchAndBound:
+
+BranchAndBound
+==============
+
+This class is an optimizer factory which creates a new branch-and-bound algorithm.
+It can be used to create customized branch-and-bound algorithms with a large degree of freedom.
+
+.. seealso::
+
+    If you are not familiar with optimizers and optimizer factories, please refer to :ref:`this page <api_optimizers>`.
+
+.. admonition:: Example
+
+    Here, we create a simple branch-and-bound algorithm where branching is done on integer variables which are being
+    relaxed. Each node is solved by the external solver GLPK. Nodes are selected according to the "best-bound"
+    rule while variables are selected according to the "most-infeasible" branching rule.
+
+    The created algorithm also incorporates sub-tree exploration of maximum depth 2.
+
+    .. code-block::
+
+        model.use(
+            BranchAndBound()
+                .with_node_optimizer( GLPK::ContinuousRelaxation() )
+                .with_branching_rule( MostInfeasible() )
+                .with_node_selection_rule( BestBound() )
+                .with_subtree_depth(2)
+        );
+
+.. doxygenclass:: idol::BranchAndBound

_sources/api/optimizers/branch-and-bound/BranchAndBoundCallback.rst.txt

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+.. _api_BranchAndBoundCallback:
+
+BranchAndBoundCallback
+======================
+
+This class can be used to create callbacks to run on idol's :ref:`branch-and-bound implementation <api_BranchAndBound>`.
+
+.. warning::
+
+    BranchAndBoundCallback-s is an *advanced* feature.
+
+    Please, make sure that what you are trying do cannot be done with
+    a :ref:`solver-independent callback <api_Callback>` first, or with pre-existing callbacks, e.g.,
+    :ref:`UserCutCallback <api_UserCutCallback>` or :ref:`LazyCutCallback <api_LazyCutCallback>`.
+
+    The advantage of using a :ref:`BranchAndBoundCallback <api_BranchAndBoundCallback>` instead of a standard
+    solver-independent :ref:`Callback <api_Callback>` lies in the possibility to access specific information regarding
+    the execution of the branch-and-bound algorithm. For instance, accessing a node's information, or the current
+    relaxation model being solved.
+
+.. admonition:: Example
+
+    Here is an example of callback which prints out the event triggering it and, when the event corresponds to `NodeLoaded`,
+    prints the node's model to be solved.
+
+    .. code-block::
+
+        class MyCallback : public BranchAndBoundCallbackFactory<NodeInfo> {
+        public:
+            class Strategy : public BranchAndBoundCallback<NodeInfo> {
+            protected:
+                void operator()(CallbackEvent t_event) override {
+
+                    std::cout << "MyCallback is called for " << t_event << std::endl;
+
+                    if (t_event != NodeLoaded) {
+                        return;
+                    }
+
+                    std::cout << "The problem being solve at node " << node().id() << std::endl;
+                    std::cout << relaxation() << std::endl;
+
+                }
+            };
+
+            BranchAndBoundCallback<NodeInfo> *operator()() override {
+                return new Strategy();
+            }
+
+            [[nodiscard]] BranchAndBoundCallbackFactory<NodeInfo> *clone() const override {
+                return new MyCallback(*this);
+            }
+        };
+
+    Then, this callback can be used as follows.
+
+    .. code-block::
+
+        model.use(
+            BranchAndBound()
+                .with_node_optimizer(GLPK::ContinuousRelaxation())
+                .with_branching_rule(MostInfeasible())
+                .with_node_selection_rule(DepthFirst())
+                .with_callback(MyCallback());
+        );
+
+.. hint::
+
+    By default, most of the objects returned by BranchAndBoundCallback methods are const. If you wish to access non-const
+    versions (e.g., if you want to perform non-standard updates to the relaxed model or want to change the node's current
+    information manually), you should use the advanced interface obtained by calling ``BranchAndBoundCallback::advanced_interface``.
+
+.. doxygenclass:: idol::BranchAndBoundCallback
+    :protected-members:

_sources/api/optimizers/branch-and-bound/branching-rules/MostInfeasible.rst.txt

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+.. _api_MostInfeasible:
+
+MostInfeasible
+==============
+
+.. doxygenclass:: idol::MostInfeasible

_sources/api/optimizers/branch-and-bound/branching-rules/index.rst.txt

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+.. _api_branching_rules:
+
+Branching rules
+===============
+
+.. toctree::
+    :maxdepth: 2
+    :glob:
+
+    MostInfeasible

_sources/api/optimizers/branch-and-bound/index.rst.txt

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+.. _api_branch_and_bound:
+
+Branch-And-Bound algorithms
+===========================
+
+.. toctree::
+    :maxdepth: 2
+    :glob:
+
+    BranchAndBound
+    branching-rules/index
+    node-selection-rules/index
+    BranchAndBoundCallback

_sources/api/optimizers/branch-and-bound/node-selection-rules/BestBound.rst.txt

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+.. _api_BestBound:
+
+BestBound
+=========
+
+.. doxygenclass:: idol::BestBound

_sources/api/optimizers/branch-and-bound/node-selection-rules/BreadthFirst.rst.txt

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+.. _api_BreadthFirst:
+
+BreadthFirst
+============
+
+.. doxygenclass:: idol::BreadthFirst

_sources/api/optimizers/branch-and-bound/node-selection-rules/DepthFirst.rst.txt

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+.. _api_DepthFirst:
+
+DepthFirst
+==========
+
+.. doxygenclass:: idol::DepthFirst

_sources/api/optimizers/branch-and-bound/node-selection-rules/WorstBound.rst.txt

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+.. _api_WorstBound:
+
+WorstBound
+==========
+
+.. doxygenclass:: idol::WorstBound

_sources/api/optimizers/branch-and-bound/node-selection-rules/index.rst.txt

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+.. _api_node_selection_rules:
+
+Node selection rules
+====================
+
+.. toctree::
+    :maxdepth: 2
+    :glob:
+
+    BestBound
+    WorstBound
+    DepthFirst
+    BreadthFirst