Safe Zeroth-Order Optimization Using Quadratic Local Approximations

arXiv2303.16659MaRDI QIDQ6431276

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Publication date: 29 March 2023

Abstract: 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 $eta$-KKT pair (a property reflecting how close a primal-dual pair is to the exact KKT condition) within $O(1/et{a}^2)$ 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.

Has companion code repository: https://github.com/odetojsmith/szo-qq

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