Full Nesterov–Todd step infeasible interior-point method for symmetric optimization

Gu, Guoyong; Zangiabadi, Maryam; Roos, C.

doi:10.1016/j.ejor.2011.02.022

Cited by 83 publications

(63 citation statements)

References 18 publications

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“…A future research may focus on some new analysis of the algorithm which yields some larger value of θ . -Roos' full-Newton step IIPM was extended to semidefinite optimization (SDO) by Mansouri and Roos [23], to symmetric optimization (SO) by Gu et al [24] and to LCP by Mansouri et al [25]. An extension of large-update FIPMs based on kernel functions to SDO was presented by El Ghami [10].…”

Section: Discussionmentioning

confidence: 99%

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Infeasible Interior-Point Methods for Linear Optimization Based on Large Neighborhood

Asadi

Roos

2015

J Optim Theory Appl

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In this paper, we design a class of infeasible interior-point methods for linear optimization based on large neighborhood. The algorithm is inspired by a full-Newton step infeasible algorithm with a linear convergence rate in problem dimension that was recently proposed by the second author. Unfortunately, despite its good numerical behavior, the theoretical convergence rate of our algorithm is worse up to square root of problem dimension.

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Section: Discussionmentioning

confidence: 99%

“…This yields the loose iteration bound given by (44). This slender value of θ is obtained because of some difficulties in the analysis of the algorithm which uses the largest value of θ , satisfying (24), to assure that Ψ (v) = O(n). This value of θ is much smaller than the best value we may choose.…”

Section: Discussionmentioning

confidence: 99%

Infeasible Interior-Point Methods for Linear Optimization Based on Large Neighborhood

Asadi

Roos

2015

J Optim Theory Appl

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“…A more detailed review can be found in [2,11,12,29]. Definition 2.1 A pair (V , •) is called Jordan algebra iff V is a finite-dimensional vector space over R and • : V × V → V is bilinear form (product) with properties…”

Section: Preliminariesmentioning

confidence: 99%

“…Subsequently, primal-dual IPMs for SCLO were analyzed by Alizadeh and Schmieta [9,10]. In their Ph.D. theses (directed by the second author of this paper) Vieira [11] analyzed kernel-based IPMs for SCLO and Gu [12] analyzed full-Newton step IPMs for SCLO. While there is an extensive literature on IPMs for LCPs over the non-negative orthant (see for example [1,[13][14][15][16][17][18][19][20][21], to mention just a few), there are fewer results on LCPs over the cone of semidefinite matrices (see for example [22][23][24]), and even less so for LCP over general symmetric cones.…”

Section: Introductionmentioning

confidence: 99%

Kernel-Based Interior-Point Methods for Monotone Linear Complementarity Problems over Symmetric Cones

Lešaja

Roos

2011

J Optim Theory Appl

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We present an interior-point method for monotone linear complementarity problems over symmetric cones (SCLCP) that is based on barrier functions which are defined by a large class of univariate functions, called eligible kernel functions. This class is fairly general and includes the classical logarithmic function, the self-regular functions, as well as many non-self-regular functions as special cases. We provide a unified analysis of the method and give a general scheme on how to calculate the iteration bounds for the entire class. We also calculate the iteration bounds of both large-step and short-step versions of the method for ten frequently used eligible kernel functions. For some of them we match the best known iteration bound for large-step methods, while for short-step methods the best iteration bound is matched for all cases. The paper generalizes results of Lesaja and Roos (SIAM J. Optim. 20(6):3014-3039, 2010) from P * (κ)-LCP over the non-negative orthant to monotone LCPs over symmetric cones.

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“…After accomplishing a few centering steps for the new perturbed problem, it obtains strictly feasible iterates close enough to central path of the new perturbed problems. This algorithm have extensively extended to other optimization problems, e.g., [2,7,[11][12][13]. Subsequently, some authors have tried to improve the Roos's infeasible algorithm, see for example [4,5].…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Primal-Dual Full-Newton Step Infeasible Interior-Point Algorithm for Linear Optimization

Asadi¹,

Mansouri²

2016

Bulletin of the Korean Mathematical Society

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Abstract. In this paper, we improve the full-Newton step infeasible interior-point algorithm proposed by Mansouri et al. [6]. The algorithm takes only one full-Newton step in a major iteration. To perform this step, the algorithm adopts the largest logical value for the barrier update parameter θ. This value is adapted with the value of proximity function δ related to (x, y, s) in current iteration of the algorithm. We derive a suitable interval to change the parameter θ from iteration to iteration. This leads to more flexibilities in the algorithm, compared to the situation that θ takes a default fixed value.

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Full Nesterov–Todd step infeasible interior-point method for symmetric optimization

Cited by 83 publications

References 18 publications

Infeasible Interior-Point Methods for Linear Optimization Based on Large Neighborhood

Infeasible Interior-Point Methods for Linear Optimization Based on Large Neighborhood

Kernel-Based Interior-Point Methods for Monotone Linear Complementarity Problems over Symmetric Cones

An Adaptive Primal-Dual Full-Newton Step Infeasible Interior-Point Algorithm for Linear Optimization

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