On a class of controlled differential variational inequalities

Abstract

By using various analytical and topological tools, weak sharp solutions are investigated for a class of controlled differential variational inequality involving convex functionals defined by path-independent curvilinear integrals. In order to illustrate the main results, an application is also provided.

Keywords:

• Controlled variational inequality
• weak sharp solution
• convex path-independent curvilinear integral functional
• minimum principle sufficiency property
• dual gap-type functional

2010 Mathematics Subject Classifications:

• 49J40
• 49J50
• 65K10
• 26B25
• 90C30
• 49K20

Acknowledgments

The present research was financially supported by University Politehnica of Bucharest, Bucharest, Romania (Grant No. MA51-18-01). Some of the results included in this paper were presented at the international conference ‘The 6th World Congress on Global Optimization’, July 8–10, Metz, France, 2019.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

The present research was financially supported by University Politehnica of Bucharest, Bucharest, Romania (Grant No. MA51-18-01).