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pro vyhledávání: '"Muramatsu, Masakazu"'
Let $({\bf P},{\bf D})$ be a primal-dual pair of SDPs with a nonzero finite duality gap. Under such circumstances, ${\bf P}$ and ${\bf D}$ are weakly feasible and if we perturb the problem data to recover strong feasibility, the (common) optimal valu
Externí odkaz:
http://arxiv.org/abs/2304.04433
We consider primal-dual pairs of semidefinite programs and assume that they are ill-posed, i.e., both primal and dual are either weakly feasible or weakly infeasible. Under such circumstances, strong duality may break down and the primal and dual mig
Externí odkaz:
http://arxiv.org/abs/1912.09696
Akademický článek
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Autor:
Muramatsu, Masakazu, Kitahara, Tomonari, Lourenço, Bruno F., Okuno, Takayuki, Tsuchiya, Takashi
We point out that Chubanov's oracle-based algorithm for linear programming [5] can be applied almost as it is to linear semi-infinite programming (LSIP). In this note, we describe the details and prove the polynomial complexity of the algorithm based
Externí odkaz:
http://arxiv.org/abs/1809.10340
In this work we present an extension of Chubanov's algorithm to the case of homogeneous feasibility problems over a symmetric cone K. As in Chubanov's method for linear feasibility problems, the algorithm consists of a basic procedure and a step wher
Externí odkaz:
http://arxiv.org/abs/1702.01421
Publikováno v:
SIAM Journal on Optimization, Volume 28 (3), 2018
We present FRA-Poly, a facial reduction algorithm (FRA) for conic linear programs that is sensitive to the presence of polyhedral faces in the cone. The main goals of FRA and FRA-Poly are the same, i.e., finding the minimal face containing the feasib
Externí odkaz:
http://arxiv.org/abs/1512.02549
The objective of this work is to study weak infeasibility in second order cone programming. For this purpose, we consider a relaxation sequence of feasibility problems that mostly preserve the feasibility status of the original problem. This is used
Externí odkaz:
http://arxiv.org/abs/1509.05168
Publikováno v:
Optimization Methods and Software, 36:2-3, 425-471, 2021
We suppose the existence of an oracle which solves any semidefinite programming (SDP) problem satisfying Slater's condition simultaneously at its primal and dual sides. We note that such an oracle might not be able to directly solve general SDPs even
Externí odkaz:
http://arxiv.org/abs/1507.08065
In this article, we present a geometric theoretical analysis of semidefinite feasibility problems (SDFPs). This is done by decomposing a SDFP into smaller problems, in a way that preserves most feasibility properties of the original problem. With thi
Externí odkaz:
http://arxiv.org/abs/1507.06843
Publikováno v:
Optimization Methods and Software, 31, 1, 134 --156, 2016
We consider a property of positive polynomials on a compact set with a small perturbation. When applied to a Polynomial Optimization Problem (POP), the property implies that the optimal value of the corresponding SemiDefinite Programming (SDP) relaxa
Externí odkaz:
http://arxiv.org/abs/1304.0065