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Vietnam
Journal of Mathematics 37:2&3 (2009) 191-223
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Parametric Optimization Problems and Parametric
Variational Inequalities
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Nguyen Dong Yen
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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).
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2000 Mathematics Subject Classification: 90C31, 49J40,
49J53.
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Keywords: Fermat Rule, parametric optimization
problem, parametric variational inequality, multifunction, continuity,
Lagrange multiplier, Karush-Kuhn-Tucker point set.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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