Hao Wang – Optimization Online

A momentum-based linearized augmented Lagrangian method for nonconvex constrained stochastic optimization

Published: 2022/08/11, Updated: 2024/03/20

Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming augmented Lagrangian function, functional constraint, momentum, nonconvex optimization, oracle complexity, stochastic gradient

Nonconvex constrained stochastic optimization has emerged in many important application areas. Subject to general functional constraints it minimizes the sum of an expectation function and a nonsmooth regularizer. Main challenges arise due to the stochasticity in the random integrand and the possibly nonconvex functional constraints. To address these issues we propose a momentum-based linearized augmented … Read more

An Inexact First-order Method for Constrained Nonlinear Optimization

Published: 2018/09/15

Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Nonlinear Optimization convex composite optimization, exact penalty functions, first-order methods, large-scale constrained 13 problems, nonlinear optimization, sequential linear optimization

The primary focus of this paper is on designing inexact first-order methods for solving large-scale constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the computational cost needed for each iteration. A penalty parameter updating strategy during the subproblem solve enables the algorithm to automatically detect infeasibility. Global … Read more

A Dynamic Penalty Parameter Updating Strategy for Matrix-Free Sequential Quadratic Optimization

Published: 2018/03/25

Constrained Nonlinear Optimization, Nonlinear Optimization alternating direction method, convex composite optimization, coordinate descent methods, exact penalty functions, nonlinear optimization, sequential quadratic programming

This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation of the search direction during each iteration, for which we consider the use of matrix-free methods. In particular, we develop a method … Read more