GENERALIZED CONTINGENT EPIDERIVATIVES IN SET-VALUED OPTIMIZATION: OPTIMALITY CONDITIONS
Johannes Jahn, Akhtar Ali Khan · Numerical Functional Analysis and Optimization · 2002
Necessary and sufficient optimality conditions are given for various optimality notions in set-valued optimization. These optimality conditions are given by employing the generalized contingent epiderivative and the weak contingent epiderivative of the objective set-valued map and the set-valued map defining the constraints. The known Lagrange multiplier rule and the so-called Zowe-Kurcyusz-Robinson (cf. Robinson, S.M. Stability Theory for Systems of Inequalities. II, Differentiable Nonlinear Systems. SIAM J. Numer. Anal. 1976, 13, 497–513. Zowe, J.; Kurcyusz, S. Regularity and Stability for the Mathematical Programming Problem in Banach spaces, Appl. Math. Optim 1979, 5, 49–62.) regularity condition are extended using these differentiability notions.