Modified Line Search Sequential Quadratic Methods for Equality-Constrained Optimization with Unified Global and Local Convergence Guarantees

TL;DR

This paper introduces a modified line search sequential quadratic programming method for nonlinear equality-constrained optimization, ensuring global and local convergence, and extends it to stochastic objectives with practical inexact variants.

Contribution

It presents a novel line search SQP method with convergence guarantees and extends it to stochastic objectives, including a practical inexact matrix-free implementation.

Findings

Method achieves global convergence and local superlinear convergence.

Numerical results demonstrate high efficiency and effectiveness.

Extension to stochastic objectives broadens applicability.

Abstract

In this paper, we propose a method that has foundations in the line search sequential quadratic programming paradigm for solving general nonlinear equality constrained optimization problems. The method employs a carefully designed modified line search strategy that utilizes second-order information of both the objective and constraint functions, as required, to mitigate the Maratos effect. Contrary to classical line search sequential quadratic programming methods, our proposed method is endowed with global convergence and local superlinear convergence guarantees. Moreover, we extend the method and analysis to the setting in which the constraint functions are deterministic but the objective function is stochastic or can be represented as a finite-sum. We also design and implement a practical inexact matrix-free variant of the method. Finally, numerical results illustrate the efficiency and efficacy of the method.