A Feasible Method for Constrained Derivative-Free Optimization

This paper explores a method for solving constrained optimization problems when the derivatives of the objective function are unavailable, while the derivatives of the constraints are known. We allow the objective and constraint function to be nonconvex. The method constructs a quadratic model of th...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-02
Main Authors: Xuan, Melody Qiming, Nocedal, Jorge
Format: Article
Language:English
Subjects:
Constraint modelling
Interpolation
Nonlinear programming
Optimization
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper explores a method for solving constrained optimization problems when the derivatives of the objective function are unavailable, while the derivatives of the constraints are known. We allow the objective and constraint function to be nonconvex. The method constructs a quadratic model of the objective function via interpolation and computes a step by minimizing this model subject to the original constraints in the problem and a trust region constraint. The step computation requires the solution of a general nonlinear program, which is economically feasible when the constraints and their derivatives are very inexpensive to compute compared to the objective function. The paper includes a summary of numerical results that highlight the method's promising potential.
ISSN:2331-8422