Duality theorems for convex programming without constraint qualification
- 1 February 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- Vol. 36 (2) , 253-266
- https://doi.org/10.1017/s144678870002468x
Abstract
Invoking a recent characterization of Optimality for a convex programming problem with finite dimensional range without any constraint qualification given by Borwein and Wolkowicz, we establish duality theorems. These duality theorems subsume numerous earlier duality results with constraint qualifications. We apply our duality theorems in the case of the objective function being the sum of a positively homogeneous, lower-semi-continuous, convex function and a subdifferentiable convex function. We also study specific problems of the above type in this setting.Keywords
This publication has 15 references indexed in Scilit:
- Duality theorems and an optimality condition for non-differentiable convex programmingJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1982
- Characterization of optimality for the abstract convex program with finite dimensional rangeJournal of the Australian Mathematical Society, 1980
- A duality theorem for nondifferentiable convex programming with operatorial constraintsBulletin of the Australian Mathematical Society, 1980
- More on subgradient dualityJournal of Mathematical Analysis and Applications, 1979
- A class of programming problems whose objective function contains a normJournal of Approximation Theory, 1978
- A subgradient duality theoremJournal of Mathematical Analysis and Applications, 1977
- Sufficient Fritz John optimality conditions for nondifferentiable convex programmingThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1976
- A programming problem with anLpnorm in the objective functionThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1976
- A class of nondifferentiable mathematical programming problemsJournal of Mathematical Analysis and Applications, 1974
- Extension of Fenchel’ duality theorem for convex functionsDuke Mathematical Journal, 1966