An extended extremal principle with applications to multi-objective optimization

B. S. Mordukhovich, J. S. Treiman and Q. J. Zhu


Abstract: We develop an extended version of the extremal principle in variational
analysis that can be treated as a variational counterpart of the classical separation
results in the case of nonconvex sets and plays an important role in the generalized
differentiation theory and its applications to optimization-related problems. The main
difference between the conventional extremal principle and the extended version developed
below is that, instead of the translation of sets involved in the extremal systems, we
allow deformations. The new version seems to be more flexible in various applications and
covers, in particular, multiobjective optimization problems with general preference
relations. In this way we obtain new necessary optimality conditions for constrained
problems of multiobjective optimization with nonsmooth data and also for multiplayer
multiobjective games.

 

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