EFFICIENCY CONDITIONS FOR NONSMOOTH VECTOR EQUILIBRIUM PROBLEMS

The purpose of this monograph is to present necessary and sufficient conditions for solutions of nonsmooth vector equilibrium problems via convexificators and primal and dual second-order Fritz John necessary conditions for weak efficiency of nonsmooth constrained vector equilibrium problems in terms of P\'ales-Zeidan second-order directional derivatines. Since the vector equilibriium problem includes as crucial special cases vector variational inequality problem, vector optimization problem, we present efficiency conditions for solutions of nonsmooth vector equilibrium problem togethor with nonsmooth vector variational inequality problem and nonsmooth vector optimization problem.