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Mathematics > Optimization and Control

arXiv:1812.10278 (math)
[Submitted on 26 Dec 2018 (v1), last revised 24 Feb 2020 (this version, v2)]

Title:Primal-dual interior-point Methods for Semidefinite Programming from an algebraic point of view, or: Using Noncommutativity for Optimization

Authors:Konrad Schrempf
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Abstract:Since more than three decades, interior-point methods proved very useful for optimization, from linear over semidefinite to conic (and partly beyond non-convex) programming; despite the fact that already in the semidefinite case (even when strong duality holds) "hard" problems are known. We shade a light on a rather surprising restriction in the non-commutative world (of semidefinite programming), namely "commutative" paths and propose a new family of solvers that is able to use the full richness of "non-commutative" search directions: (primal) feasible-interior-point methods. Beside a detailed basic discussion, we illustrate some variants of "non-commutative" paths and provide a simple implementation for further (problem specific) investigations.
Comments: 49 pages, 10 figures, 3 tables, 5 Octave/Matlab files; slightly updated version
Subjects: Optimization and Control (math.OC)
MSC classes: 90C22, 90C51 (Primary), 90C05 (Secondary)
Cite as: arXiv:1812.10278 [math.OC]
  (or arXiv:1812.10278v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1812.10278

Submission history

From: Konrad Schrempf [view email]
[v1] Wed, 26 Dec 2018 10:25:09 UTC (101 KB)
[v2] Mon, 24 Feb 2020 16:06:50 UTC (102 KB)
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