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Vietnam Journal of Mathematics 37:2&3 (2009) 191-223 

Parametric Optimization Problems and Parametric Variational Inequalities

Nguyen Dong Yen

Abstract.  This survey is a re-edited form of a plenary lecture on Optimization Theory and Scientific Computing at the Seventh Congress of Vietnamese Mathematicians, August 4--8, 2008, Quy Nhon University, Quy Nhon, Binh Dinh. It describes some aspects of the author's and his coauthors' research on optimization problems and variational inequalities during the last 18 years (1992--2009). The focus point is made on parametric problems and qualitative results (stability, sensitivity of the solution set and the alike objects when the problem undergoes small perturbations).

2000 Mathematics Subject Classification: 90C31, 49J40, 49J53.

Keywords: Fermat Rule, parametric optimization problem, parametric variational inequality, multifunction, continuity, Lagrange multiplier, Karush-Kuhn-Tucker point set.

Vietnam Academy of Science and Technology & Vietnamese Mathematical Society
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