On Closedness Conditions, Strong Separation, and Convex Duality | Zendy

Miklós Ujvári | Zendy

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On Closedness Conditions, Strong Separation, and Convex Duality

Author(s) -

Miklós Ujvári

Publication year - 2013

Publication title -

acta cybernetica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.143

H-Index - 18

eISSN - 2676-993X

pISSN - 0324-721X

DOI - 10.14232/actacyb.21.2.2013.5

Subject(s) - mathematics , duality (order theory) , polyhedron , convex analysis , convex cone , strong duality , fenchel's duality theorem , regular polygon , pure mathematics , duality gap , lagrangian , convex set , convex polytope , cone (formal languages) , convex optimization , combinatorics , mathematical optimization , optimization problem , geometry , algorithm

In the paper, we describe various applications of the closedness and duality theorems of [7] and [8]. First, the strong separability of a polyhedron and a linear image of a convex set is characterized. Then, it is shown how stability conditions (known from the generalized Fenchel-Rockafellar duality theory) can be reformulated as closedness conditions. Finally, we present a generalized Lagrange duality theorem for Lagrange programs described with cone-convex/cone-polyhedral mappings. Mathematics Subject Classifications (2000). 90C46, 90C25, 52A41.

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