Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term

Cai, Xinzhong; Wang, Guoqiang; Ghami, Mohamed El; Yue, Yujing

doi:10.1155/2014/710158

Cited by 22 publications

(26 citation statements)

References 7 publications

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“…This is an interesting question left for future work. Heuristic algorithm Exact algorithm Heuristic algorithm Exact algorithm In this section, we introduce the Kernel function approach for interior-point methods [2,16,3] and discuss its connection with our approach. Let Ψ(v) : R n ++ → R be a strictly convex function such that Ψ(v) is minimal at v = e and Ψ(e) = 0.…”

Section: Resultsmentioning

confidence: 99%

Primal-dual entropy-based interior-point algorithms for linear optimization

Karimi

Luo²,

Tunçel

2017

RAIRO-Oper. Res.

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We propose a family of search directions based on primal-dual entropy in the context of interior-point methods for linear optimization. We show that by using entropy based search directions in the predictor step of a predictor-corrector algorithm together with a homogeneous self-dual embedding, we can achieve the current best iteration complexity bound for linear optimization. Then, we focus on some wide neighborhood algorithms and show that in our family of entropy based search directions, we can find the best search direction and step size combination by performing a plane search at each iteration. For this purpose, we propose a heuristic plane search algorithm as well as an exact one. Finally, we perform computational experiments to study the performance of entropy-based search directions in wide neighborhoods of the central path, with and without utilizing the plane search algorithms.

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Section: Resultsmentioning

confidence: 99%

Primal-dual entropy-based interior-point algorithms for linear optimization

Karimi

Luo²,

Tunçel

2017

RAIRO-Oper. Res.

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“…The extension to P * (κ)-linear complementarity problem was also presented in [10]. The obtained complexity for large-update improve significantly the complexity obtained in [6,7]. In this paper we consider kernel functions of the form…”

Section: Our Kernel Function and Some Of Its Propertiesmentioning

confidence: 93%

Primal-Dual Algorithms for Semidefinit Optimization Problems Based on Generalized Trigonometric Barrier Function

Ghami¹

2017

Int. J. of Pure and Appl. Math.

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Recently, M. Bouafoa, et al. [5] (Journal of optimization Theory and Applications, August, 2016),investigated a new kernel function which differs from the self-regular kernel functions. The kernel function has a trigonometric Barrier Term. In this paper we generalize the analysis presented in the above paper for Semidefinit Optimization Problems (SDO). It is shown that the interior-point methods based on this function for large-update methods, the iteration bound is improved significantly. For small-update interior point methods the iteration bound is the best currently known bound for primal-dual interior point methods. The analysis for SDO deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.

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“…They provided a simple and unified computational scheme for the complexity analysis of primal-dual kernel function based (IPMs) for (LO). Consequently, a series of eligible kernel functions are considered for various optimization problems and complementarity problems, see, e.g., [15,16,17,18]. For a survey, we refer to the monograph [19] on the subject and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization

Luo¹

2016

AJAM

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Abstract:In this paper, a class of large-update primal-dual interior-point methods for semidefinite optimization based on a parametric kernel function are presented. The proposed kernel function is not only used for determining the search directions but also for measuring the distance between the given iterate and the center for the algorithms. By means of the Nesterov and Todd scaling scheme, the currently best known iteration bounds for large-update methods is established.

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Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term

Cited by 22 publications

References 7 publications

Primal-dual entropy-based interior-point algorithms for linear optimization

Primal-dual entropy-based interior-point algorithms for linear optimization

Primal-Dual Algorithms for Semidefinit Optimization Problems Based on Generalized Trigonometric Barrier Function

A Parametric Kernel Function Yielding the Best Known Iteration Bound of Interior-Point Methods for Semidefinite Optimization

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