Well-posedness for equilibrium problems and for optimization problems with equilibrium constraints. (English) Zbl 1179.49007

Fang, Ya-Ping; Hu, Rong; Huang, Nan-Jing

Comput. Math. Appl. 55, No. 1, 89-100 (2008).

Summary: We generalize the concepts of well-posedness to equilibrium problems and to optimization problems with equilibrium constraints. We establish some metric characterizations of well-posedness for equilibrium problems and for optimization problems with equilibrium constraints. We prove that under suitable conditions, the well-posedness is equivalent to the existence and uniqueness of solutions. The corresponding concepts of well-posedness in the generalized sense are also introduced and investigated for equilibrium problems and for optimization problems with equilibrium constraints.

MSC:

49J40	Variational inequalities
49K40	Sensitivity, stability, well-posedness

Keywords:

equilibrium problems; optimization problems with equilibrium constraints; well-posedness; metric characterizations; monotonicity

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