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Well-posedness for parametric vector equilibrium problems with applications. (English) Zbl 1161.90479
Summary: We study the parametric well-posedness for vector equilibrium problems and propose a generalized well-posed concept for equilibrium problems with equilibrium constraints (EPEC in short) in topological vector spaces setting. We show that under suitable conditions, the well-posedness defined by approximating solution nets is equivalent to the upper semicontinuity of the solution mapping of perturbed problems. Further, since optimization problems and variational inequality problems are special cases of equilibrium problems, related variational problems can be adopted under some equivalent conditions. Finally, we also study the relationship between well-posedness and parametric well-posedness.
MSC:
90C29Multi-objective programming; goal programming
90C48Programming in abstract spaces
90C31Sensitivity, stability, parametric optimization
46N10Applications of functional analysis in optimization and programming
47N10Applications of operator theory in optimization, convex analysis, programming, economics
49J40Variational methods including variational inequalities