Scalar Lagrange Multiplier Rules for Set-Valued Problems in Infinite-Dimensional Spaces
This paper deals with Lagrange multiplier rules for constrained set-valued optimization problems in infinite-dimensional spaces, where the multipliers appear as scalarization functions of the maps instead of the derivatives. These rules provide necessary conditions for weak minimizers under hypotheses of stability, convexity, and directional compactness. Counterexamples show that the hypotheses are minimal.
lagrange multiplier rules set-valued optimization contingent (epi)derivatives vector optimization