For an inequality system defined by an infinite family of proper convex functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications. Under the new constraint qualifications, we provide necessary and/or sufficient conditions for the KKT rules to hold.
New Constraint Qualification and Conjugate Duality for Composed Convex Optimization Problems
✍ Scribed by R. I. Boţ; S. M. Grad; G. Wanka
- Publisher
- Springer
- Year
- 2007
- Tongue
- English
- Weight
- 376 KB
- Volume
- 135
- Category
- Article
- ISSN
- 0022-3239
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📜 SIMILAR VOLUMES
In this paper we discuss the connections of four generalized constraint qualifications for set-valued vector optimization problems with constraints. Then some K-T type necessary and sufficient optimality conditions are derived, in terms of the contingent epiderivatives.
## Abstract In this paper we work in separated locally convex spaces where we give equivalent statements for the formulae of the conjugate function of the sum of a convex lower‐semicontinuous function and the precomposition of another convex lower‐semicontinuous function which is also __K__ ‐increa