Well-posedness for vector quasiequilibria. (English) Zbl 1176.49030

Anh, Lam Quoc; Khanh, Phan Quoc; Van, Dang Thi My; Yao, Jen-Chih

Taiwanese J. Math. 13, No. 2B, 713-737 (2009).

Summary: We consider well-posedness under perturbations of vector quasiequilibrium and bilevel-equilibrium problems. This kind of well-posedness relates Hadamard and Tikhonov well-posedness notions to sensitivity analysis and we apply techniques of the latter to establish sufficient conditions for wellposedness under perturbations. We also propose several new semicontinuity and quasiconvexity notions to weaken the imposed assumptions. Our results are new or include as special cases recent existing results. Many examples are provided for the illustration purpose.

MSC:

49K40	Sensitivity, stability, well-posedness
90C31	Sensitivity, stability, parametric optimization
65K99	Numerical methods for mathematical programming, optimization and variational techniques

Keywords:

well-posedness; unique well-posedness; perturbations; vector quasi-equilibrium problems; bilevel problems; cone-quasi semicontinuity; cone-level convexity