A generalized gradient projection method based on a new working set for minimax optimization problems with inequality constraints

Abstract

Combining the techniques of the working set identification and generalized gradient projection, we present a new generalized gradient projection algorithm for minimax optimization problems with inequality constraints. In this paper, we propose a new optimal identification function, from which we provide a new working set. At each iteration, the improved search direction is generated by only one generalized gradient projection explicit formula, which is simple and could reduce the computational cost. Under some mild assumptions, the algorithm possesses the global and strong convergence. Finally, the numerical results show that the proposed algorithm is promising.

The global convergence properties of an adaptive QP-free method without a penalty function or a filter for minimax optimization

“…For (2), there are many algorithms can be used such as gradient projection [5], interior point method [6], trust-region [7], sequential quadratic programming(SQP) [8], penalty function [9], filter methods [10] or QP-free method [11], etc.…”

Numerical solution of linear-quadratic optimal control problems for switching systems

“…Examples of switching systems can be found in the area of engineering, chemical processes, automotive systems and military services. The published results in the literature can be mainly classified into two categories; one is theoretical [3,4,6,7,9,10,[16][17][18][19]22] and practical [2,8,11,[13][14][15]20,21]. The very earliest result which is proved a maximum principe for hybrid system for autonomous switching system is in [20].…”