2 results
Characterization of optimality for the abstract convex program with finite dimensional range
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- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 30 / Issue 4 / April 1981
- Published online by Cambridge University Press:
- 09 April 2009, pp. 390-411
- Print publication:
- April 1981
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- Article
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This paper presents characterizations of optimality for the abstract convex program
when S is an arbitrary convex cone in a finite dimensional space, Ω is a convex set and p and g are respectively convex and S-convex (on Ω). These characterizations, which include a Lagrange multiplier theorem and do not presume any a priori constraint qualification, subsume those presently in the literature.
Facial reduction for a cone-convex programming problem
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- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 30 / Issue 3 / February 1981
- Published online by Cambridge University Press:
- 09 April 2009, pp. 369-380
- Print publication:
- February 1981
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- Article
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- You have access
- Export citation
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In this paper we study the abstract convex program
where S is an arbitrary convex cone in a finite dimensional space, Ω is a convex set and p and g are respectively convex and S (on Ω). We use the concept of a minimal cone for (P) to correct and strengthen a previous characterization of optimality for (P), see Theorem 3.2. The results presented here are used in a sequel to provide a Lagrange multiplier theorem for (P) which holds without any constraint qualification.
