On the multiplier rules

Abstract

We establish new results of first-order necessary conditions of optimality for finite-dimensional problems with inequality constraints and for problems with equality and inequality constraints, in the form of John’s theorem and in the form of Karush–Kuhn–Tucker’s theorem. In comparison with existing results, we weaken assumptions of continuity and of differentiability.

Keywords:

• Multiplier rule
• Karush–Kuhn–Tucker theorem

AMS Subject Classifications:

• 90C30
• 49K99

Notes

No potential conflict of interest was reported by the author.