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

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

An Inexact First-order Method for Constrained Nonlinear 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

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