A New Wide Neighborhood Primal–Dual Infeasible-Interior-Point Method for Symmetric Cone Programming

Liu, Hongwei; Yang, Ximei; Liu, Changhe

doi:10.1007/s10957-013-0303-y

Cited by 41 publications

(8 citation statements)

References 24 publications

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“…Usually finding such a starting point is difficult. In that case an infeasible interior-point method (IIPM) [12] with an arbitrary positive starting point may be a good alternative. Roos [17] first proposed a full-Newton step IIPM for solving LO with the best known iteration bound for IIPMs, which uses only full-Newton steps.…”

mentioning

confidence: 99%

A full-modified-Newton step $ O(n) $ infeasible interior-point method for the special weighted linear complementarity problem

Chi

Wan

Zhang

2022

JIMO

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The weighted complementarity problem (wCP) can be applied to a large variety of equilibrium problems in science, economics and engineering. Since formulating an equilibrium problem as a wCP may lead to highly efficient algorithms for its numerical solution, wCP is a nontrivial generalization of the complementarity problem. In this paper we consider a special weighted linear complementarity problem (wLCP), which is the more general optimization of the Fisher market equilibrium problem. A full-modified-Newton infeasible interior-point method (IIPM) for the special wLCP is proposed. The algorithm reformulates the central path of the perturbed problem as an equivalent system of equations, and uses only full-Newton steps at each iteration, so-called a feasibility step (i.e., a full-modified-Newton step) and several usual centering steps. The polynomial complexity of the algorithm is as good as the best known iteration bound for these types of IIPMs in linear optimization.

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confidence: 99%

A full-modified-Newton step $ O(n) $ infeasible interior-point method for the special weighted linear complementarity problem

Chi

Wan

Zhang

2022

JIMO

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“…Faybusovich [7] made the first attempt to generalize IPMs from LO to SO using EJAs and associated symmetric cones. Consequently, several efficient IPMs for SO have been developed (see, e.g., [8][9][10][11][12][13][14][15]). For an overview of the relevant results, we refer to the recent book on this subject [16] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Improved Complexity Analysis of Full Nesterov–Todd Step Feasible Interior-Point Method for Symmetric Optimization

Wang

Kong

Tao

et al. 2014

J Optim Theory Appl

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In this paper, an improved complexity analysis of full Nesterov-Todd step feasible interior-point method for symmetric optimization is considered. Specifically, we establish a sharper quadratic convergence result using several new results from Euclidean Jordan algebras, which leads to a wider quadratic convergence neighbourhood of the central path for the iterates in the algorithm. Furthermore, we derive the currently best known iteration bound for full Nesterov-Todd step feasible interiorpoint method.

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“…The reason for choosingr c in equation (3.7) is that the extra computational effort is marginal compared to the computation of Newton search directions with choosing any classical terms such as e and τ µe −x •s (see [14,18,25]).…”

Section: Central Path and Its Ellipsoidal Approximationmentioning

confidence: 99%

An Arc Search Interior-Point Algorithm for Monotone Linear Complementarity Problems over Symmetric Cones

Pirhaji

Mansouri

Amin

2018

Mathematical Modelling and Analysis

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An arc search interior-point algorithm for monotone symmetric cone linear complementarity problem is presented. The algorithm estimates the central path by an ellipse and follows an ellipsoidal approximation of the central path to reach an "-approximate solution of the problem in a wide neighborhood of the central path. The convergence analysis of the algorithm is derived. Furthermore, we prove that the algorithm has the complexity bound O ( p rL) using Nesterov-Todd search direction and O (rL) by the xs and sx search directions. The obtained iteration complexities coincide with the best-known ones obtained by any proposed interior- point algorithm for this class of mathematical problems.

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A New Wide Neighborhood Primal–Dual Infeasible-Interior-Point Method for Symmetric Cone Programming

Cited by 41 publications

References 24 publications

A full-modified-Newton step $ O(n) $ infeasible interior-point method for the special weighted linear complementarity problem

A full-modified-Newton step $ O(n) $ infeasible interior-point method for the special weighted linear complementarity problem

Improved Complexity Analysis of Full Nesterov–Todd Step Feasible Interior-Point Method for Symmetric Optimization

An Arc Search Interior-Point Algorithm for Monotone Linear Complementarity Problems over Symmetric Cones

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