A guide to conic optimisation and its applications

Letchford, Adam N.; Parkes, Andrew J.

doi:10.1051/ro/2018034

Cited by 7 publications

(8 citation statements)

References 92 publications

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“…Consider a finite non-empty subset W of the simplex T defined in (4). Without loss of generality, we suppose that the elements of the set W are indexed as follows:…”

Section: Problem Statement Basic Notation and Some Preliminary Resultsmentioning

confidence: 99%

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Regularization Algorithms for Linear Copositive Programming Problems: An Approach Based on the Concept of Immobile Indices

Kostyukova

Tchemisova

2022

Algorithms

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In this paper, we continue an earlier study of the regularization procedures of linear copositive problems and present new algorithms that can be considered as modifications of the algorithm described in our previous publication, which is based on the concept of immobile indices. The main steps of the regularization algorithms proposed in this paper are explicitly described and interpreted from the point of view of the facial geometry of the cone of copositive matrices. The results of the paper provide a deeper understanding of the structure of feasible sets of copositive problems and can be useful for developing a duality theory for these problems.

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“…Consider a finite non-empty subset W of the simplex T defined in (4). Without loss of generality, we suppose that the elements of the set W are indexed as follows:…”

Section: Problem Statement Basic Notation and Some Preliminary Resultsmentioning

confidence: 99%

“…Copositive models exist for many important applications, including N P-hard problems. For references on the motivations and applications of CoP, see, e.g., [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Regularization Algorithms for Linear Copositive Programming Problems: An Approach Based on the Concept of Immobile Indices

Kostyukova

Tchemisova

2022

Algorithms

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“…and there is no duality gap for problem (20) and its dual problem in the form (21) with K * 0 replaced by K * 0 . Note that the cones K 0 and K * 0 are explicitly described in terms of indices (15) and this is an advantage of the presented here approach over that described in 3.1. The only drawback of the regularization procedure described here is the following:…”

Section: One-step Regularization Based On the Concept Of Immobile Ind...mentioning

confidence: 99%

“…to apply the one-step regularization , one needs to know the finite number of indices (15) which are the vertices of the set conv T im .…”

Section: One-step Regularization Based On the Concept Of Immobile Ind...mentioning

confidence: 99%

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Face reduction and the immobile indices approaches to regularization of linear Copositive Programming problems

Kostyukova¹,

Tchemisova²

2021

Preprint

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The paper is devoted to the regularization of linear Copositive Programming problems which consists of transforming a problem to an equivalent form, where the Slater condition is satisfied and the strong duality holds. We describe here two regularization algorithms based on the concept of immobile indices and an understanding of the important role these indices play in the feasible sets' characterization. These algorithms are compared to some regularization procedures developed for a more general case of convex problems and based on a facial reduction approach. We show that the immobile-index-based approach combined with the specifics of copositive problems allows us to construct more explicit and detailed regularization algorithms for linear Copositive Programming problems than those already available.

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