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Attention

This code has been merged to the main branch of TensCalc and will no longer be mantained.

MinmaxNewton

The code in this repository implements the algorithm and numerical examples from our paper Newton and interior-point methods for (constrained) nonconvex-nonconcave minmax optimization with stability guarantees.

The code is implemented in MATLAB and requires installing TensCalc (and its dependencies). TensCalc is used as a backend to compute the symbolic differentiation and to generate optimize code, either MATLAB or C++.

The bulk of the algorithm is implemented in two files:

  • generate_tens_functions.m parses the symbolic optimization problem and generates the code to compute the appropriate gradients and Hessians.
  • ip_newton_minmax.m implements the interior-point (and consequently, Newton method) described in the paper, with the appropriate Hessian modifications.

The two files in the main folder of the repository, benchmark.m and pursuit_evasion.m, implement the numerical examples from our paper.