Optimality conditions and sensitivity analysis in parametric nonconvex minimax programming (Q6607020)

The authors consider the following parametric nonconvex minimax programming problem (PNMPP) on Banach spaces \(X,Y\):\N\[\N\min_{y \in G(x)} \max_{k \in K} \phi_k(x,y),\N\]\Nwhere \(x \in X\) is a parameter, \(G:X \rightarrow K\) is a given multi-function, \(K\) is a finite set, \( \phi_k: X \times Y \rightarrow R \cup \{-\infty, \infty \},~k \in K \).\N\NConcepts of local and global optimal solutions of PNMPP are defined. The corresponding necessary and sufficient optimality conditions are proved using Morduchovich subdifferential. The results are applied further to multi-objective optimization problems. An illustrative example demonstrating the obtained theoretical results is provided.