CBO for Saddle Point Problems (CBO-SP)

Implementation of a consensus-based optimization method for saddle point problems (CBO-SP).

CBO-SP is a novel multi-particle metaheuristic derivative-free optimization method capable of provably finding global Nash equilibria. Following the idea of swarm intelligence, the method employs a group of interacting particles, which perform a minimization over one variable and a maximization over the other.

Version 1.0

Date 23.12.2022

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R e f e r e n c e s

Consensus-Based Optimization for Saddle Point Problems

https://arxiv.org/abs/2212.12334

by

• Hui   H u a n g   (University of Graz),
• Jinniao   Q i u   (University of Calgary),
• Konstantin   R i e d l   (Technical University of Munich, Munich Center for Machine Learning)

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D e s c r i p t i o n

MATLAB implementation of a consensus-based optimization method for saddle point problems.

For the reader's convenience we describe the folder structure in what follows:

BenchmarkFunctions

• objective_function.m: objective function generator
• ObjectiveFunctionPlot.m: plotting routine for objective function

EnergyBasedCBOAnalysis

• analyses: convergence and parameter analyses of CBO-SP
  • CBOSPNumericalExample.m: testing script
• CBOSP: code of CBO-SP optimizer
  • compute_consensus.m: computation of consensus point
  • CBOSP_update: one CBO-SP step
  • CBOSP.m: CBO-SP optimizer
• visualizations: visualization of the CBO-SP dynamics
  • CBOSPIllustrative.m: Illustration of the CBO-SP at work

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C i t a t i o n s

@article{CBOSPQiuHuangRiedl,
      title = {Consensus-Based Optimization for Saddle Point Problems},
     author = {Jinniao Qiu and Hui Huang and Konstantin Riedl},
       year = {2022},
    journal = {arXiv preprint arXiv:2212.12334},
}