We introduce a primal-dual interior point algorithm for convex quadratic semidefinite optimization. This algorithm is based on an extension of the technique presented in the work of Zhang et al. for linear optimizatio...
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We introduce a primal-dual interior point algorithm for convex quadratic semidefinite optimization. This algorithm is based on an extension of the technique presented in the work of Zhang et al. for linear optimization. The symmetrization of the search direction is based on the Nesterov-Todd scaling scheme. Our analysis demonstrates that this method solves efficiently the problem within polynomial time. Notably, the short-step algorithm achieves the best-known iteration bound, namely O(nlogn epsilon)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(\sqrt{n}\log \frac{n}{\varepsilon })$$\end{document}-iterations. The numerical experiments conclude that the newly proposed algorithm is not only polynomial but requires a number of iterations clearly lower than that obtained theoretically.
In this paper,we propose an interior-point algorithm based on a wide neighborhood for convex quadratic semidefinite optimization *** the Nesterov–Todd direction as the search direction,we prove the convergence analys...
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In this paper,we propose an interior-point algorithm based on a wide neighborhood for convex quadratic semidefinite optimization *** the Nesterov–Todd direction as the search direction,we prove the convergence analysis and obtain the polynomial complexity bound of the proposed *** the algorithm belongs to the class of large-step interior-point algorithms,its complexity coincides with the best iteration bound for short-step interior-point *** algorithm is also implemented to demonstrate that it is efficient.
In this paper, we propose a new corrector-predictor algorithm for convex quadratic semidefinite optimization problem based on a new proximity measure. The search direction is obtained by an equivalent algebraic transf...
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In this paper, we propose a new corrector-predictor algorithm for convex quadratic semidefinite optimization problem based on a new proximity measure. The search direction is obtained by an equivalent algebraic transformation of the centering equation. At each iteration, the algorithm is composed of a corrector step and a predictor step. The predictor step uses line search schemes requiring the reduction of the duality gap, while the corrector step is used to restore the iterates to the neighborhood of the central path. Finally, the algorithm has the currently best-known iteration complexity.
Kernel functions play an important role in the design and analysis of primal-dual interior-point algorithms. They are not only used for determining the search directions but also for measuring the distance between the...
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Kernel functions play an important role in the design and analysis of primal-dual interior-point algorithms. They are not only used for determining the search directions but also for measuring the distance between the given iterate and the mu-center for the algorithms. In this paper we present a unified kernel function approach to primal-dual interior-point algorithms for convex quadratic semidefinite optimization based on the Nesterov and Todd symmetrization scheme. The iteration bounds for large- and small-update methods obtained are analogous to the linear optimization case. Moreover, this unifies the analysis for linear, convexquadratic and semidefiniteoptimizations.
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 ...
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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 semidefiniteoptimization analogue. (C) 2013 Elsevier Inc. All rights reserved.
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