An improved version of Chubanov's method for solving a homogeneous feasibility problem

Roos, C.

doi:10.1080/10556788.2017.1368509

Cited by 19 publications

(41 citation statements)

References 11 publications

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“…Recently, an interesting new polynomial-time algorithm was proposed by Chubanov [3,4,5]. Related studies include, for instance, [2,10,15,16]. In this paper, we develop a word-by-word extension of Chubanov's algorithm to second-order cone programming [1,6,12,13,14,17].…”

Section: Introductionmentioning

confidence: 99%

An extension of Chubanov's polynomial-time linear programming algorithm to second-order cone programming

Kitahara

Tsuchiya

2017

Optimization Methods and Software

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Section: Introductionmentioning

confidence: 99%

An extension of Chubanov's polynomial-time linear programming algorithm to second-order cone programming

Kitahara

Tsuchiya

2017

Optimization Methods and Software

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“…Like [20] and its predecessors [6,10], both [8] and [7], as well as this paper, can be seen as enhancements of the classical relaxation method [1,16]. Chubanov's work has also been revisited and extended by various sets of authors [4,15,21]. The numerical experiments reported in the articles by Roos [21] and by Li, Roos, and Terlaky [15] provide promising evidence of the computational effectiveness of Chubanov's method [8] and related variants.…”

Section: Introductionmentioning

confidence: 63%

Solving Conic Systems via Projection and Rescaling

Peña

Soheili

2016

Math. Program.

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We propose a simple projection and rescaling algorithm to solve the feasibility problem find x ∈ L ∩ Ω, where L and Ω are respectively a linear subspace and the interior of a symmetric cone in a finite-dimensional vector space V . This projection and rescaling algorithm is inspired by previous work on rescaled versions of the perceptron algorithm and by Chubanov's projectionbased method for linear feasibility problems. As in these predecessors, each main iteration of our algorithm contains two steps: a basic procedure and a rescaling step. When L ∩ Ω = ∅, the projection and rescaling algorithm finds a pointis attained when L ∩ Ω contains the center of the symmetric cone Ω.We describe several possible implementations for the basic procedure including a perceptron scheme and a smooth perceptron scheme. The perceptron scheme requires O(r 4 ) perceptron updates and the smooth perceptron scheme requires O(r 2 ) smooth perceptron updates, where r stands for the Jordan algebra rank of V . IntroductionWe propose a simple algorithm based on projection and rescaling operations to solve the feasibility problem findwhere L and Ω are respectively a linear subspace and the interior of a symmetric cone in a finite-dimensional vector space V . Problem (1) is fundamental in optimization as it encompasses a large class of feasibility problems. For example, for A ∈ R m×n and b ∈ R m , the problem Ax = b, x > 0 can be formulated as (1) by taking L = {(x, t) ∈ R n+1 : Ax − tb = 0} and Ω = R n+1 ++ . For A ∈ R m×n , c ∈ R n , the problem A

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“…This difference is likely due to the different basic procedures used in [15] and in our numerical experiments. The rescaling method in [15] uses a variant of the von Neumann algorithm as its basic procedure while we use the smooth perceptron scheme.…”

Section: Other Experimentsmentioning

confidence: 97%

“…However, despite their interesting theoretical guarantees, there has been limited work on the computational effectiveness of the projection and rescaling algorithm as well as other methods based on rescaling. As far as we know, only the articles by Li et al [11] and by Roos [15] report numerical results on implementations of some variants of Chubanov's projection and rescaling algorithm. This paper documents a MATLAB implementation of an enhanced version of the projection and rescaling algorithm from [14].…”

Section: Introductionmentioning

confidence: 99%

Computational performance of a projection and rescaling algorithm

Peña

Soheili

2019

Optimization Methods and Software

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This paper documents a computational implementation of a projection and rescaling algorithm for finding most interior solutions to the pair of feasibility problemswhere L denotes a linear subspace in R n and L ⊥ denotes its orthogonal complement. The projection and rescaling algorithm is a recently developed method that combines a basic procedure involving only low-cost operations with a periodic rescaling step. We give a full description of a MATLAB implementation of this algorithm and present multiple sets of numerical experiments on synthetic problem instances with varied levels of conditioning. Our computational experiments provide promising evidence of the effectiveness of the projection and rescaling algorithm. Our MATLAB code is publicly available. Furthermore, the simplicity of the algorithm makes a computational implementation in other environments completely straightforward. *

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An improved version of Chubanov's method for solving a homogeneous feasibility problem

Cited by 19 publications

References 11 publications

An extension of Chubanov's polynomial-time linear programming algorithm to second-order cone programming

An extension of Chubanov's polynomial-time linear programming algorithm to second-order cone programming

Solving Conic Systems via Projection and Rescaling

Computational performance of a projection and rescaling algorithm

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