Relaxation in nonconvex optimal control for nonlinear evolution hemivariational inequalities. (December 2019)

• Record Type: Journal Article
• Authors: Bin, Maojun; Liu, Zhenhai
• Is Part Of: Nonlinear analysis. Volume 50(2019)
• Page Start: 613
• Page End: 632
• Publication Date: 2019-12
• Subjects: Hemivariational inequality -- Optimal control -- Relaxation property -- Nonconvex constraint -- Feedback control; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.05.013
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The purpose of this paper is to consider a control system of nonlinear evolution hemivariational inequalities with mixed nonconvex constraints on the control. First, we investigate the relaxed problem for the hemivariational inequalities systems with feedback control and the integrand convexicated with respect to the control. Second, under some general conditions, the existence of optimal solution of the relaxed problem for hemivariational inequalities control systems is proved. Furthermore, we show that for every optimal solution there exists a minimizing sequence of the original problem converging to the optimal solution with respect to trajectories and the functional in appropriate topologies simultaneously. Finally, an example is provided to illustrate the main results.