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Complexity analysis and numerical implementation of a full-Newton step interior-point algorithm for LCCO

NUMERICAL algorithms 2015年第2期70卷 393-405页

作者： Achache, Mohamed Goutali, Moufida Univ Ferhat Abbas Setif1 Lab Math Fondamentales & Numer Setif Algeria Univ Ferhat Abbas Setif1 Fac Sci Dept Math Setif Algeria

In this paper, we present a primal-dual interior point algorithm for linearly constrained convex optimization (LCCO). The algorithm uses only full-Newton step to update iterates with an appropriate proximity measure for controlling feasible iterations near the central path during the solution process. The favorable polynomial complexity bound for the algorithm with short-step method is obtained, namely O(root n log n/epsilon) which is as good as the linear and convex quadratic optimization analogue. Numerical results are reported to show the efficiency of the algorithm.

关键词： Linearly constrained convex optimization Interior point methods short-step primal-dual algorithms Complexity of algorithms

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A full-Newton step feasible weighted primal-dual interior point algorithm for monotone LCP

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AFRIKA MATEMATIKA 2015年第1-2期26卷 139-151页

作者： Achache, Mohamed Khebchache, Radia Univ Ferhat Abbas Setif1 Lab Math Fondament & Numer Setif Algeria Univ Ferhat Abbas Setif1 Fac Sci Dept Math Setif Algeria

In this paper, we propose a weighted short-step primal-dual interior point algorithm for solving monotone linear complementarity problem (LCP). The algorithm uses at each interior point iteration a full-Newton step and the strategy of the central path to obtain an epsilon-approximate solution of LCP. This algorithm yields the best currently well-known theoretical complexity iteration bound, namely, O(root n log n/epsilon) which is as good as the bound for the linear optimization analogue. The implementation of the algorithm and the algorithm in Wang et al. (Fuzzy Inform Eng 54:479-487, 2009) is done followed by a comparison between these two obtained numerical results.

关键词： Linear complementarity problems Interior point methods short-step primal-dual algorithms Complexity of algorithms

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A full Nesterov-Todd-step feasible primal-dual interior point algorithm for convex quadratic semi-definite optimization

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APPLIED MATHEMATICS AND COMPUTATION 2014年第0期231卷 581-590页

作者： Achache, Mohamed Guerra, Loubna Univ Ferhat Abbas Lab Math Fondamentales & Numer Setif 1 Algeria Univ Ferhat Abbas Dept Math Fac Sci Setif 1 Algeria

In this paper, a short-step feasible primal-dual path-following interior point algorithm is proposed for solving a convex quadratic semidefinite optimization (CQSDO) problem. The algorithm uses at each iteration full Nesterov-Todd (NT) steps to find an c-approximated solution of CQSDO. The favorable iteration bound, namely O(root n log n/epsilon) is obtained for short-step method and which is as good as the linear and semidefinite optimization analogue. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Convex quadratic semidefinite optimization Interior point methods short-step primal-dual algorithms Polynomial complexity

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A polynomial-time weighted path-following interior-point algorithm for linear optimization

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ASIAN-EUROPEAN JOURNAL OF MATHEMATICS 2020年第2期13卷

作者： Achache, Mohamed Univ Ferhat Abbas Lab Math Fondamentales & Numer Setif 1 Setif 19000 Algeria

In this paper, a weighted short-step primal-dual path-following interior-point algorithm for solving linear optimization (LO) is presented. The algorithm uses at each interior-point iteration a full-Newton step, thus no need to use line search, and the strategy of the central-path to obtain an epsilon-approximated solution of LO. We show that the algorithm yields the iteration bound, namely, O(root n log n/epsilon). This bound is currently the best iteration bound for LO. Finally, some numerical results are reported in order to analyze the efficiency of the proposed algorithm.

关键词： Linear optimization problems interior-point methods short-step primal-dual algorithms complexity of algorithms

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