黄方艳;张明望;黄正伟;

• 1:三峡大学理学院
• 2:三峡大学经济与管理学院

摘要(Abstract)：

最近,Salahi对线性规划提出了一个基于新的自适应参数校正策略的Mehrotra型预估-校正算法,该策略使其在不使用安全策略的情况下,证明了算法的多项式迭代复杂界.本文将这一算法推广到半定规划的情形.通过利用Zhang的对称化技术,得到了算法的多项式迭代复杂界,这与求解线性规划的相应算法有相同的迭代复杂性阶.

关键词(KeyWords)： Mehrotra型算法;半定规划;迭代复杂性;对称化技术

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金(71471102)

作者(Authors): 黄方艳;张明望;黄正伟;

参考文献(References)：

• [1]Karmarkar N K.A new polynomial-time algorithm for linear programming[J].Combinatorica,1984,4:373-395.
• [2]Mehrotra S.On the implementation of a primal-dual interior point method[J].SIAM Journal on Optimization,1992,2:575-601.
• [3]Andersen E D,Andersen K D.The Mosek Interior Point Optimizer for Linear Programming:an Implementation of the Homogeneous Algorithm[M].Holland:Kluwer Academic Publishers,2000:197-232.
• [4]Vanderbei R J.Loqo:an interior-point code for quadratic programming[J].Optimization Methods and Software,1999,12:451-488.
• [5]Zhang Y.Solving large-scale linear programmes by interior point methods under the Matlab environment[J].Optimization Methods and Software,1999,10:1-31.
• [6]Salahi M,Peng J,Terlaky T.On Mehrotra-type predictor-corrector algorithms[J].SIAM Journal on Optimization,2007,18(4):1377-1397.
• [7]Salahi M,Mahdavi-Amiri N.Polynomial time second order Mehrotra-type predictor-corrector algorithms[J].Applied Mathematics and Computation,2006,183:646-658.
• [8]Salahi M,Terlaky T.Postponing the choice of the barrier parameter in Mehrotra-type predictor-corrector algorithms[J].European Journal of Operational Research,2007,182:502-513.
• [9]Salahi M.New Barrier Parameter Updating technique in mehrotra-type algorithm[J].Bulletin of the Iranian Mathematical Society,2010,36(2):99-108.
• [10]Zhang Y.On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming[J].SIAM Journal on Optimization,1998,8:365-386.
• [11]Koulaei H M,Terlaky T.On the extension of a mehrotra-type algorithm for semidefinite optization[R].Hamilton,Ontario,Canada:Mc Master University,2007.
• [12]Zhang M W.A second order Mehrotra-type predictor-corrector algorithm for semidefinite optimization[J].Journal of Systems Science Complexity,2012,25:1108-1121.
• [13]Roos C,Terlaky T.Theory and Algorithms for Linear Optimization:an Interior Point Approach[M].Chichester,UK:John Wiley and Sons,1997.
• [14]Klerk De E.Aspects of Semidefinite Programming:Interior Point Algorithms and Selected Applications[M].Dordrecht,The Netherlands:Kluwer Academic Publishers,2002.
• [15]Nesterov Y E,Nemirovsky A S.Interior Point Methods in Convex Programming:Theory and Applications[M].Philadelphia:Society for Industrial and Applied Mathematics,1994.
• [16]Wolkowicz H,Saigal R,Vandenberghe L.Handbook of Semidefinite Programming,Theory,Algorithms,and Applications[M].The Netherlands:Kluwer Academic Publishers,2000.
• [17]Horn R A,Johnson C R.Matrix Analysis[M].New York:Cambridge University Press,1990.
• [18]Wright S J.Primal-Dual Interior-Point Methods[M].USA:SIAM,1997.
• [19]Wang G Q,Bai Y Q,Roos C.Primal-dual interior-point algorithms for semi-definite optimization based on a simple kernel function[J].Journal of Mathematical Modelling and Algorithms,2005,4(4):409-433.