Generalized contingent epiderivatives in set-valued optimization: optimality conditions - Jahn, Johannes; Khan, Akhtar Ali (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.
UnivIS-Import:2015-03-09:Pub.2002.nat.dma.pama21.genera
Keywords: Aubin property; Contingent cone; Generalized contingent epiderivative; Lagrange multipliers; Optimality conditions; Regularity conditions; Set-valued optimization