2023/03/29 by Baiwei Guo, Guo, Baiwei, Yuning Jiang +5 · 3 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Bandit Algorithms Research #Advanced Optimization Algorithms Research #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2303.16659
openalex publication_date 2023/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper addresses black-box smooth optimization problems, where the objective and constraint functions are not explicitly known but can be queried. The main goal of this work is to generate a sequence of feasible points converging towards a KKT primal-dual pair. Assuming to have prior knowledge on the smoothness of the unknown objective and constraints, we propose a novel zeroth-order method that iteratively computes quadratic approximations of the constraint functions, constructs local feasible sets and optimizes over them. Under some mild assumptions, we prove that this method returns an η-KKT pair (a property reflecting how close a primal-dual pair is to the exact KKT condition) within O(1/η2) iterations. Moreover, we numerically show that our method can achieve faster convergence compared with some state-of-the-art zeroth-order approaches. The effectiveness of the proposed approach is also illustrated by applying it to nonconvex optimization problems in optimal control and power system operation.