New optimality criteria for convex continuous-time problems of vector optimization

Abstract

In this paper, vector continuous-time programming problems with inequality type of constraints are considered. All the results are obtained under convexity assumptions. The main tool employed in the derivation of the zero order optimality conditions is a new version of theorem of the alternative in functional spaces. To apply the alternative theorem, a certain regularity condition must be satisfied. No differentiability assumption is imposed.

Keywords:

• Continuous-time programming
• vector problems
• optimality conditions

2010 Mathematics Subject Classifications:

• 90C30
• 90C46
• 90C29

Acknowledgments

The authors would like to thank two anonymous referees whose valuable comments improved the presentation considerably.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia [grants 174015 and 174020].