2024/06/17 by Albert S. Berahas, Berahas, Albert S., Raghu Bollapragada +3
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2406.11144
openalex publication_date 2024/06/17 · openalex created_date 2024/06/19 · openalex updated_date 2026/07/28
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.