Consensus-Based Algorithms for Stochastic Optimization Problems

SIAM Journal on Optimization, vol. 35, pp. 2572–2598

Abstract

Abstract. We address an optimization problem where the cost function is the expectation of a random mapping. To tackle the problem two approaches based on the approximation of the objective function by consensus-based particle optimization methods on the search space are developed. The resulting methods are mathematically analyzed using a mean-field approximation, and their connection is established. Several numerical experiments show the validity of the proposed algorithms and investigate their rates of convergence.

Authors 2

1. Sabrina Bonandin Aachen Institute for Geometry and Practical Mathematics

   RWTH Aachen University

   Affiliation as printed

   Institute for Geometry and Practical Mathematics, RWTH Aachen University, Aachen 52062, Germany

2. Michaël Herty Aachen Institute for Geometry and Practical Mathematics

   RWTH Aachen University · University of Pretoria

   Affiliation as printed

   Institute for Geometry and Practical Mathematics, RWTH Aachen University, Aachen 52062, Germany, and Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield 0028, South Africa