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Duality aspects in convex conic programming

Maria Trnovska(trnovska***at***fmph.uniba.sk)
Jakub Hrdina(hrdina8***at***uniba.sk)

Abstract: In this paper we study strong duality aspects in convex conic programming over general convex cones. It is known that the duality in convex optimization is linked with specific theorems of alternatives. We formulate and prove strong alternatives to the existence of the relative interior point in the primal (dual) feasible set. We analyze the relation between the boundedness of the optimal solution sets and the existence of the relative interior points in the feasible set. We also provide conditions under which the duality gap is zero and the optimal solution sets are unbounded. As a consequence, we obtain several alternative conditions that guarantee the strong duality between primal and dual convex conic programs.

Keywords: convex conic programming, strong duality, generalized theorems of alternatives

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Faculty of mathematics, physics and informatics, Comenius University in Bratislava

Download: [PDF]

Entry Submitted: 11/19/2021
Entry Accepted: 11/20/2021
Entry Last Modified: 11/19/2021

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