G. Pataki. Strong duality in conic linear programming: facial reduction and extended duals. In Computa- tional and analytical mathematics, volume 50 of Springer Proc. Math. Stat., pages 613-634. Springer, New York, 2013.G. Pataki, "Strong duality in conic linear programming: facial reduction...
Strong duality as an optimality condition is investigated. A new approach to duality in the form of positive extendability of linear functionals is proposed. A necessary and sufficient condition for duality in the form of a boundedness test of a related linear program is developed. Elaborating on...
NOTES ON FARKAS’ LEMMA AND THE STRONG DUALITY THEOREM FOR LINEAR PROGRAMMING Let A be an m×n real matrix. We work throughout with column vectors x ∈ R n and y ∈ R m . Farkas’ Lemma. Let b ∈ R m . Either there exists x ∈ R n such that x ≥ 0 and Ax = b, or ...
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Strong Duality in Conic Linear Programming and Its Applications 翻译结果2复制译文编辑译文朗读译文返回顶部 Strong Duality in Conic Linear Programming and Its Applications 翻译结果3复制译文编辑译文朗读译文返回顶部 Strong Duality in Conic Linear Programming and Its Applications ...
Minimax linear fractional programming with uncertaintyWe develop a duality theory for minimax fractional programming problems in the face of data uncertainty both in the objective and constraints. Following the framework of robust optimization, we establish strong duality between the robust counterpart of ...
Strong duality has been proven for the integer linear programming problem, where a super-additive function prices out the activities and closes the duality... S Holm - 《Optimization Methods & Software》 被引量: 0发表: 1994年 A Customized Augmented Lagrangian Method for Block-Structured Integer ...
Throughout this paper, the authors introduce a new condition, defined by Assumption S′, which establishes a necessary and sufficient condition for the validity of the strong duality between a convex optimization problem and its Lagrange dual. This work will be focused on the context of emptiness...
Solutions Chapter 5 SECTION 5.1 5.1.4 w w w Throughout this exercise we will use the fact that strong duality holds for convex quadratic problems with linear constraints (cf. Section 3.4). The problem of finding the minimum distance from the origin to a line is written as min 1 2 kxk2...
where \(C \subseteq E\) is a nonempty, closed and convex set in a real Banach space E with dual \(E^{*}\), \(\langle\cdot,\cdot\rangle\) denotes the duality paring on E, and \(A:E \to E^{*}\) is a given operator. We denote the set of solutions of the VI by \(\ma...