LEVITIN-POLYAK WELL-POSEDNESS FOR GENERALIZED QUASI-VARIATIONAL INCLUSION AND DISCLUSION PROBLEMS AND OPTIMIZATION PROBLEMS WITH CONSTRAINTS

In this paper, Levitin-Polyak well-posedness for generalized quasivariational inclusion and disclusion problems are introduced and studied. Necessary and sufficient conditions for Levitin-Polyak well-posedness of these problems are proved. Moreover, Levitin-Polyak well-posedness for optimization pro...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 16; no. 1; pp. 237 - 257
Main Authors Wang, San-Hua, Huang, Nan-Jing
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.02.2012
Subjects
Banach space
Mathematical vectors
Nash equilibrium
Scalars
Variational inequalities
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Summary:In this paper, Levitin-Polyak well-posedness for generalized quasivariational inclusion and disclusion problems are introduced and studied. Necessary and sufficient conditions for Levitin-Polyak well-posedness of these problems are proved. Moreover, Levitin-Polyak well-posedness for optimization problems with generalized quasi-variational inclusion problems, generalized quasi-variational disclusion problems and scalar generalized quasi-equilibrium problems as constraints are also given under some suitable conditions. 2010Mathematics Subject Classification: 49J27, 49J40. Key words and phrases: Levitin-Polyak well-posedness, Generalized quasi-variational inclusion problem, Generalized quasi-variational disclusion problem, Optimization problem, Approximating solution sequence.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500406539