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An Arc Search Infeasible Interior-Point Algorithm for Symmetric Optimization Using a New Wide Neighborhood

An Arc Search Infeasible Interior-Point Algorithm for Symmetric Optimization Using a New Wide... In this paper, we propose an infeasible interior-point algorithm for symmetric optimization problems using a new wide neighborhood and estimating the central path by an ellipse. In contrast of most interior-point algorithms for symmetric optimization which search an ε $\varepsilon$ -optimal solution of the problem in a small neighborhood of the central path, our algorithm searches for optimizers in a new wide neighborhood of the ellipsoidal approximation of central path. The convergence analysis of the algorithm is shown and it is proved that the iteration bound of the algorithm is O ( r log ε − 1 ) $O ( r\log\varepsilon^{-1} ) $ which improves the complexity bound of the recent proposed algorithm by Liu et al. (J. Optim. Theory Appl., 2013, https://doi.org/10.1007/s10957-013-0303-y ) for symmetric optimization by the factor r 1 2 $r^{\frac{1}{2}}$ and matches the currently best-known iteration bound for infeasible interior-point methods. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

An Arc Search Infeasible Interior-Point Algorithm for Symmetric Optimization Using a New Wide Neighborhood

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References (23)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-018-0164-3
Publisher site
See Article on Publisher Site

Abstract

In this paper, we propose an infeasible interior-point algorithm for symmetric optimization problems using a new wide neighborhood and estimating the central path by an ellipse. In contrast of most interior-point algorithms for symmetric optimization which search an ε $\varepsilon$ -optimal solution of the problem in a small neighborhood of the central path, our algorithm searches for optimizers in a new wide neighborhood of the ellipsoidal approximation of central path. The convergence analysis of the algorithm is shown and it is proved that the iteration bound of the algorithm is O ( r log ε − 1 ) $O ( r\log\varepsilon^{-1} ) $ which improves the complexity bound of the recent proposed algorithm by Liu et al. (J. Optim. Theory Appl., 2013, https://doi.org/10.1007/s10957-013-0303-y ) for symmetric optimization by the factor r 1 2 $r^{\frac{1}{2}}$ and matches the currently best-known iteration bound for infeasible interior-point methods.

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: Mar 6, 2018

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