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A POLYNOMIAL PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR convex quadratic programming

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Acta Mathematica Scientia 2006年第2期26卷 265-270页

作者：余谦黄崇超江燕 Institute of Systems Engineering of Wuhan University Wuhan 430072 China School of Mathematics and Statistics Wuhan University Wuhan 430072China

This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step, where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has O（√nL） iteration complexity which is the best result for convex quadratic programming so far.

关键词： convex quadratic programming predictor-corrector interior-point algorithm

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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

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SOLVING convex quadratic programming BY POTENTIAL-REDUCTION INTERIOR-POINT ALGORITHM

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2001年第1期2卷 67-71页

作者：梁昔明马龙华钱积新 College of Information Science & EngineeringCentral South UniversityChangshaChina Institute of Systems Engineering National Lab of Industrial Control TechnologyZhejiang UniversityHangzhouChina

The solution of quadratic programming problems is an important issue in the field of mathematical programming and industrial applications. In this paper, we solve convex quadratic programming by a potential-reduction interior-point algorithm. It is proved that the potential-reduction interior-point algorithm is globally convergent. Some numerical experiments were made.

关键词： potential-reduction interior-point algorithm convex quadratic programming convergence numerical experiments

凸二次规划的一个改进的Mehrotra型预估-校正算法

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高等学校计算数学学报 2011年第3期33卷 250-260页

作者：赵玉琴张明望周意元三峡大学理学院

引言自1984年Karmarkar提出[1]以来,内点算法成为最活跃的研究领域之一,至今取得了大量的成果.此外,人们开发了许多基于内点算法的优化软件包.预估-校正算法是最有效的内点算法之一,并且成为众多优化软件的核心算法.大部分数值实现都是基于

关键词： convex quadratic programming predictor-corrector method methrotra-type algorithm polynomial complexity.

A Feasible Decomposition Method for Constrained Equations and Its Application to Complementarity Problems

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Acta Mathematicae Applicatae Sinica 2011年第3期27卷 535-548页

作者： Xiang-li Li Hong-wei Liu Chang-he Liu Department of Mathematics Xidian University Xian 710071 China Department of Applied Mathematics Henan University of Science and Technology Luoyang 471003 China

In this paper, by analyzing the propositions of solution of the convex quadratic programming with nonnegative constraints, we propose a feasible decomposition method for constrained equations. Under mild conditions, the global convergence can be obtained. The method is applied to the complementary problems. Numerical results are also given to show the efficiency of the proposed method.

关键词： convex quadratic programming nonnegative constraints feasible decomposition method

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A Numerical Methodology for Enforcing Maximum Principles and the Non-Negative Constraint for Transient Diffusion Equations

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Communications in Computational Physics 2016年第1期19卷 53-93页

作者： K.B.Nakshatrala H.Nagarajan M.Shabouei Department of Civil&Environmental Engineering University of HoustonHoustonTexas 77204-4003USA Department of Mechanial Engineering Texas A&M UniversityCollege StationTX 77843USA.

Transient diffusion equations arise in many branches of engineering and applied sciences(e.g.,heat transfer and mass transfer),and are parabolic partial differential *** is well-known that these equations satisfy important mathematical properties like maximum principles and the non-negative constraint,which have implications in mathematical ***,existing numerical formulations for these types of equations do not,in general,satisfy maximum principles and the nonnegative *** this paper,we present a methodology for enforcing maximum principles and the non-negative constraint for transient anisotropic diffusion *** proposed methodology is based on the method of horizontal lines in which the time is discretized *** results in solving steady anisotropic diffusion equation with decay equation at every discrete *** also present other plausible temporal discretizations,and illustrate their shortcomings in meeting maximum principles and the non-negative *** proposedmethodology can handle general computational grids with no additional restrictions on the *** illustrate the performance and accuracy of the proposed methodology using representative numerical *** also perform a numerical convergence analysis of the proposed *** comparison,we also present the results from the standard singlefield semi-discrete formulation and the results froma popular software package,which all will violate maximum principles and the non-negative constraint.

关键词： Numerical heat and mass transfer maximum principles non-negative solutions anisotropic diffusion method of horizontal lines convex quadratic programming parabolic PDEs

Signal Blind Recover in Communication Systems using Support Vector Machines

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Signal Blind Recover in Communication Systems using Support ...