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Partially B-regular optimization and equilibrium problems. (English) Zbl 1341.90145
Summary: This paper introduces a concept termed partial B-regularity for a feasible solution to a bivariate constraint system and shows that this condition leads to the equivalence between the B-stationarity of a pair of lifted and unlifted programs. In particular, for an optimization problem with a univariate pseudoconvex objective function constrained by such a nonconvex bivariate system, partial B-regularity provides a sufficient condition for a B-stationary point to be globally optimal. Applications of partial B-regularity to several classes of optimization and equilibrium problems are presented; these include a lexicographic optimization problem, a nonconvex mathematical program with equilibrium constraints (MPEC) that arises from a convex implicit value-function optimization problem, and a Nash equilibrium program with equilibrium constraints.

MSC:
90C46 Optimality conditions and duality in mathematical programming
90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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