To solve unmodeled optimization problems with hard constraints, this paper proposes a novel zeroth-order approach called Safe Zeroth-order Optimization using Linear Programs (SZO-LP). The SZO-LP method solves a linear program in each iteration to find a descent direction, followed by a step length determination. We prove that, under mild conditions, the iterates of SZO-LP have an accumulation point that is also the primal of a KKT pair. We then apply SZO-LP to solve an Optimal Power Flow (OPF) problem on the IEEE 30-bus system. The results demonstrate that SZO-LP requires less computation time and samples compared to state-of-the-art approaches.
@article{arxiv.2304.01797,
title = {Safe Zeroth-Order Optimization Using Linear Programs},
author = {Baiwei Guo and Yang Wang and Yuning Jiang and Maryam Kamgarpour and Giancarlo Ferrari-Trecate},
journal= {arXiv preprint arXiv:2304.01797},
year = {2023}
}