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R. Lucchetti (2006)
Convexity and well-posed problems
G. Nürnberger (1984)
Unicity in Semi-Infinite Optimization
E. Polak (1997)
Semi-Infinite Optimization
B. Brosowski, F. Deutsch (1985)
Parametric Optimization and Approximation
M. Goberna, M. López (1998)
Linear Semi-Infinite Optimization
M. Goberna, M. López, M. Todorov (2003)
A Generic Result in Linear Semi-Infinite OptimizationApplied Mathematics and Optimization, 48
B. Bank (1983)
Non-Linear Parametric Optimization
R. Hettich, P. Zencke (1982)
Numerische Methoden der Approximation und semi-infiniten Optimierung
J.P. Aubin, H. Frankowska (1990)
Set-Valued Analysis
M. Goberna, M. López, M. Todorov (1996)
Stability Theory for Linear Inequality SystemsSIAM J. Matrix Anal. Appl., 17
M. Cánovas, D. Klatte, M. López, J. Parra (2007)
Metric Regularity in Convex Semi-Infinite Optimization under Canonical PerturbationsSIAM J. Optim., 18
S. Helbig, M. Todorov (1998)
Unicity Results for General Linear Semi-Infinite Optimization Problems Using a New Concept of Active ConstraintsApplied Mathematics and Optimization, 38
R.T. Rockafellar (1970)
Convex Analysis
M. Fajardo, M. López (1999)
Locally Farkas–Minkowski Systems in Convex Semi-Infinite ProgrammingJournal of Optimization Theory and Applications, 103
M. Goberna, M. López, M. Todorov (2003)
Extended Active Constraints in Linear Optimization with ApplicationsSIAM J. Optim., 14
M. Goberna, M. López, M. Todorov (2003)
A Sup-Function Approach to Linear Semi-Infinite OptimizationJournal of Mathematical Sciences, 116
A. Dontchev, T. Zolezzi (1993)
Well-Posed Optimization Problems
B. Craven (1984)
Non-Linear Parametric Optimization (B. Bank, J. Guddat, D. Klatte, B. Kummer and K. Tammer)Siam Review, 26
The concept of implicit active constraints at a given point provides useful local information about the solution set of linear semi-infinite systems and about the optimal set in linear semi-infinite programming provided the set of gradient vectors of the constraints is bounded, commonly under the additional assumption that there exists some strong Slater point. This paper shows that the mentioned global boundedness condition can be replaced by a weaker local condition (LUB) based on locally active constraints (active in a ball of small radius whose center is some nominal point), providing geometric information about the solution set and Karush-Kuhn-Tucker type conditions for the optimal solution to be strongly unique. The maintaining of the latter property under sufficiently small perturbations of all the data is also analyzed, giving a characterization of its stability with respect to these perturbations in terms of the strong Slater condition, the so-called Extended-Nürnberger condition, and the LUB condition.
Applied Mathematics and Optimization – Springer Journals
Published: Apr 1, 2011
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