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A FULL-NEWTON STEP INFEASIBLE INTERIOR-POINT ALGORITHM FOR P_*(κ) LINEAR COMPLEMENTARITY PROBLEM

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Journal of Systems Science & Complexity 2014年第5期27卷 1027-1044页

作者： ZHU Danhua zhang mingwang College of Science China Three Gorges University

This paper proposes a new infeasible interior-point algorithm with full-Newton steps for P_*(κ) linear complementarity problem(LCP),which is an extension of the work by Roos(SIAM ***.,2006,16(4):1110-1136).The main iteration consists of a feasibility step and several centrality *** authors introduce a specific kernel function instead of the classic logarithmical barrier function to induce the feasibility step,so the analysis of the feasibility step is different from that of Roos' *** kernel function has a finite value on the *** result of iteration complexity coincides with the currently known best one for infeasible interior-point methods for P_*(κ) *** numerical results are reported as well.

关键词： Full-Newton steps infeasible interior-point method P*(κ) linear complementarity problems polynomial complexity

New Mehrotra's second order predictor-corrector algorithm for P_*(κ) linear complementarity problems

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Journal of Systems Engineering and Electronics 2010年第4期21卷 705-712页

作者： mingwang zhang Yanli Lu College of Science China Three Gorges University Yichang 443002 R R. China

It has been shown in various papers that most interior-point algorithms for linear optimization and their analysis can be generalized to P_＊（κ） linear complementarity *** paper presents an extension of the recent variant of Mehrotra＇s second order algorithm for linear *** is shown that the iteration-complexity bound of the algorithm is O（4κ ＋ 3）√14κ ＋ 5 nlog（x0）Ts0/ε,which is similar to that of the corresponding algorithm for linear optimization.

关键词： linear complementarity problem P_*(κ)-matrix Mehrotra-type predictor-corrector algorithm polynomial complexity.

A Full-Newton Step Feasible IPM for Semidefinite Optimization Based on a Kernel Function with Linear Growth Term

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Wuhan University Journal of Natural Sciences 2020年第6期25卷 501-509页

作者： GENG Jie zhang mingwang PANG Jinjuan Mathematics Department Anhui Institute of Information TechnologyWuhu 241000AnhuiChina College of Science China Three Gorges UniversityYichang 443002HubeiChina

In this paper,we propose and analyze a full-Newton step feasible interior-point algorithm for semidefinite optimization based on a kernel function with linear growth *** kernel function is used both for determining the search directions and for measuring the distance between the given iterate and theμ-center for the *** developing a new norm-based proximity measure and some technical results,we derive the iteration bound that coincides with the currently best known iteration bound for the algorithm with small-update *** our knowledge,this result is the first instance of full-Newton step feasible interior-point method for SDO which involving the kernel function.

关键词： semidefinite optimization interior-point algorithm kernel function iteration complexity

A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function

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Wuhan University Journal of Natural Sciences 2024年第1期29卷 29-37页

作者： GENG Jie zhang mingwang ZHU Dechun Mathematics Department Anhui Institute of Information TechnologyWuhu 241000AnhuiChina College of Science China Three Gorges UniversityYichang 443002HubeiChina

In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and *** algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point ***,numerical results illustrate the efficiency of the proposed method.

关键词： interior-point algorithm weighted linear complementarity problem full-Newton step kernel function iteration complexity

A Wide Neighborhood Arc-Search Interior-Point Algorithm for Convex Quadratic Programming

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Wuhan University Journal of Natural Sciences 2017年第6期22卷 465-471页

作者： YUAN Beibei zhang mingwang HUANG Zhengwei College of Science China Three Gorges University Yichang 443002 Hubei China College of Economics and Management China Three Gorges University Yichang 443002 Hubei China

In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the entire central path. The favorable polynomial complexity bound of the algorithm is obtained, namely O（nlog（（ x^0）~TS^0/ε）） which is as good as the linear programming analogue. Finally, the numerical experiments show that the proposed algorithm is efficient.

关键词： arc-search interior-point algorithm polynomial complexity convex quadratic programming

A New Second-Order Mehrotra-Type Predictor-Corrector Algorithm for SDO

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Wuhan University Journal of Natural Sciences 2016年第2期21卷 99-109页

作者： HUANG Fangyan zhang mingwang HUANG Zhengwei College of Science China Three Gorges University College of Economics and Management China Three Gorges University

In zhang’s recent works,a second-order Mehrotra-type predictor-corrector algorithm for linear optimization was extended to semidefinite optimization and derived that the algorithm for semidefinite optimization had3/2 0 T 0O（nlog（X）gS/e）iteration complexity based on the NT direction as Newton search *** this paper,we extend the second-order Mehrotra-type predictor-corrector algorithm for linear optimization to semidefinite optimization and discuss the polynomial convergence of the algorithm by modifying the corrector direction and new *** is proved that the iteration complexity is reduced to0 0O（nlog XgS/e）,which coincides with the currently best iteration bound of Mehrotra-type predictor-corrector algorithm for semidefinite optimization.

关键词： Mehrotra-type algorithm predictor-corrector methods semidefinite optimization

Kernel Function-Based Primal-Dual Interior-Point Methods for Symmetric Cones Optimization

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Wuhan University Journal of Natural Sciences 2014年第6期19卷 461-468页

作者： ZHAO Dequan zhang mingwang College of Science China Three Gorges University

In this paper, we present a large-update primal-dual interior-point method for symmetric cone optimization（SCO） based on a new kernel function, which determines both search directions and the proximity measure between the iterate and the center path. The kernel function is neither a self-regular function nor the usual logarithmic kernel function. Besides, by using Euclidean Jordan algebraic techniques, we achieve the favorable iteration complexity O（ √r（1/2）（log r）^2 log（r/ ε））, which is as good as the convex quadratic semi-definite optimization analogue.

关键词： symmetric cones optimization Kernel function Interior-point method polynomial complexity

Interior-Point Algorithm for Linear Optimization Based on a New Kernel Function

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Wuhan University Journal of Natural Sciences 2012年第1期17卷 12-18页

作者： CHEN Donghai zhang mingwang LI Weihua College of Science China Three Gorges UniversityYichang 443002HubeiChina

In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions.

关键词： linear optimization interior-point algorithms pri- mal-dual methods kernel function polynomial complexity

A Mehrotra-Type Predictor-Corrector Algorithm for P*（κ） Linear Complementarity Problems

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Journal of Mathematical Research with Applications 2012年第3期32卷 297-312页

作者： Weihua LI,mingwang zhang,Yiyuan ZHOU College of Science,China Three Gorges University,Hubei 443002,P.R.China College of Science China Three Gorges University Hubei 443002

Mehrotra-type predictor-corrector algorithm,as one of most efficient interior point methods,has become the backbones of most optimization *** et *** a cut strategy based algorithm for linear optimization that enjoyed polynomial complexity and maintained its efficiency in *** extend their algorithm to P（κ）linear complementarity *** way of choosing corrector direction for our algorithm is different from theirs. The new algorithm has been proved to have an ο(（1+4κ）(17+19κ) √（1+2κn）log[（x）s/ε] worst case iteration complexity *** numerical experiment verifies the feasibility of the new algorithm.

关键词： P_*(κ)linear complementarity problems Mehrotra-type predictor-corrector algo- rithm polynomial iteration complexity interior point method.