An Inexact First-order Method for Constrained Nonlinear Optimization

Hao Wang(wanghao1shanghaitech.edu.cn)
Jiashan Wang(jsw1119gmail.com)
Yuyang Rong(rongyyshanghaitech.edu.cn)
Hudie Zhou(zhouhdshanghaitech.edu.cn)

Abstract: 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 convergence for both feasible and infeasible cases are proved. Complexity analysis for the KKT residual is also derived under loose assumptions. Numerical experiments exhibit the ability of the proposed algorithm to rapidly find inexact optimal solution through cheap computational cost.

Keywords: nonlinear optimization, sequential linear optimization, large-scale constrained 13 problems, exact penalty functions, convex composite optimization, first-order methods

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Convex and Nonsmooth Optimization

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Entry Submitted: 09/15/2018
Entry Accepted: 09/15/2018
Entry Last Modified: 09/15/2018

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