Constrained stochastic blackbox optimization using a progressive barrier and probabilistic estimates

• 成果类型: Article
• 署名作者: Dzahini, Kwassi Joseph; Kokkolaras, Michael; Le Digabel, Sebastien
• 署名单位: Universite de Montreal; Polytechnique Montreal; Universite de Montreal; Polytechnique Montreal; Universite de Montreal; McGill University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-022-01787-7
• 发表日期: 2023
• 页码: 675-732
• 关键词: direct search algorithm; robust optimization; pattern search; simplex-method; minimization; performance

摘要

This work introduces the StoMADS-PB algorithm for constrained stochastic blackbox optimization, which is an extension of the mesh adaptive direct-search (MADS) method originally developed for deterministic blackbox optimization under general constraints. The values of the objective and constraint functions are provided by a noisy blackbox, i.e., they can only be computed with random noise whose distribution is unknown. As in MADS, constraint violations are aggregated into a single constraint violation function. Since all function values are numerically unavailable, StoMADS-PB uses estimates and introduces probabilistic bounds for the violation. Such estimates and bounds obtained from stochastic observations are required to be accurate and reliable with high, but fixed, probabilities. The proposed method, which allows intermediate infeasible solutions, accepts new points using sufficient decrease conditions and imposing a threshold on the probabilistic bounds. Using Clarke nonsmooth calculus and martingale theory, Clarke stationarity convergence results for the objective and the violation function are derived with probability one.