Nonregular multiobjective problems: optimality conditions

Abstract

Necessary and sufficient conditions for multiobjective problems with both equality constraints and inequality constraints are presented. These conditions are applied when the constraints of the problem do not necessarily satisfy any regularity assumptions and they are based on the concept of p-regularity, introduced by Tret'yakov (1983, Necessary conditions for optimality of pth order. Control Optim.;28–35). We introduce the notion of generalized Mangasarian-Fromovitz constraint qualification. This new concept is used to obtain our results.

Keywords:

• Nonregular problems
• generalized constraint qualifications
• p-regularity

AMS Subject Classifications:

• 90C26
• 90C30
• 90C46

Disclosure statement

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