Weak stability and strong duality of a class of nonconvex infinite programs via augmented Lagrangian

Authors:
T. Q. Son;D. S. Kim;N. N. Tam
Affiliations:
Department of Natural Sciences, Nhatrang College of Education, Nhatrang, Vietnam;Department of Applied Mathematics, Pukyong National University, Busan, Korea;Department of Mathematics, University of Pedagogy of Hanoi 2, Vinh Phuc, Vietnam
Venue:
Journal of Global Optimization
Year:
2012

Citing 8
Cited 2

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Abstract

In this paper we deal with weak stability and duality of a class of nonconvex infinite programs via augmented Lagrangian. Firstly, we study a concept of weak-subdifferential of an extended real valued function on a topological linear space. Augmented Lagrangian functions and a concept of weak-stability are constructed. Next, relations between weak-stability and strong duality of problems via augmented Lagrangians are investigated. Applications for convex infinite programs are discussed. Saddle point theorems are established. An illustrative example is given.