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Connections among constrained continuous and combinatorial vector optimization. (English) Zbl 1237.90196
Summary: In this article, constrained continuous and combinatorial vector optimization problems (VOPs) are considered in the setting of finite-dimensional Euclidean spaces. Equivalence results between constrained integer and continuous VOPs are established by virtue of that between a constrained VOP and its penalized problem. Finally, one of the established equivalences is applied to derive necessary optimality conditions for a constrained integer VOP.
MSC:
90C27Combinatorial optimization
90C10Integer programming
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
49J40Variational methods including variational inequalities