Asymptotical good behavior on inequalities with completely approximate K–T concept

We characterize a wide class of regular convex functionals that are asymptotically well behaved on a convex set given by (infinite) inequalities, namely, those restricted functions whose stationary sequences (bounded or not) are minimizing ones. After showing the equivalence with the Kuhn–Tucker typ...

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Bibliographic Details
Published in:Operations research letters 2012-03, Vol.40 (2), p.134-139
Main Authors: El Maghri, M., Radi, B.
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Asymptotic properties
Calculus of variations and optimal control
Convergence
Exact sciences and technology
Expansion
Exteriors
Functionals
Inequalities
Infeasibility
KT sequences
Mathematical analysis
Mathematical programming
Mathematics
Minimizing sequences
Operational research and scientific management
Operational research. Management science
Operations research
Penalty methods
Sciences and techniques of general use
Unboundedness
Well-behavedness
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Summary:We characterize a wide class of regular convex functionals that are asymptotically well behaved on a convex set given by (infinite) inequalities, namely, those restricted functions whose stationary sequences (bounded or not) are minimizing ones. After showing the equivalence with the Kuhn–Tucker type stationarity, we prove that the class of such functions remains unchanged when the Kuhn–Tucker system is completely relaxed. This allows us to proceed for enlarging the scope of convergence of certain penalty (exterior as well as interior) methods including a new exterior penalization for infinite inequalities.
ISSN:0167-6377
1872-7468
DOI:10.1016/j.orl.2011.12.005