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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.

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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