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.