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Title: A Full-Newton Step Infeasible Interior-Point Algorithm for Linear Programming Based on a Kernel Function

Abstract

This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming, which is an extension of the work of Roos (SIAM J. Optim. 16(4):1110-1136, 2006). The main iteration of the algorithm consists of a feasibility step and several centrality steps. We introduce a kernel function in the algorithm to induce the feasibility step. For parameter p element of [0,1], the polynomial complexity can be proved and the result coincides with the best result for infeasible interior-point methods, that is, O(nlog n/{epsilon})

Authors:
 [1];  [2];  [3]
  1. Hohai University, College of Science (China), E-mail: zhyi@hhu.edu.cn
  2. Nanjing Normal University, School of Mathematics and Computer Science (China), E-mail: wysun@njnu.edu.cn
  3. University of Science and Technology of China, Department of Modern Mechanics (China), E-mail: tfbao@mail.ustc.edu.cn
Publication Date:
OSTI Identifier:
21241844
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 60; Journal Issue: 2; Other Information: DOI: 10.1007/s00245-009-9069-x; Copyright (c) 2009 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; LINEAR PROGRAMMING; POLYNOMIALS

Citation Formats

Liu Zhongyi, Sun, Wenyu, and Tian Fangbao. A Full-Newton Step Infeasible Interior-Point Algorithm for Linear Programming Based on a Kernel Function. United States: N. p., 2009. Web. doi:10.1007/S00245-009-9069-X.
Liu Zhongyi, Sun, Wenyu, & Tian Fangbao. A Full-Newton Step Infeasible Interior-Point Algorithm for Linear Programming Based on a Kernel Function. United States. doi:10.1007/S00245-009-9069-X.
Liu Zhongyi, Sun, Wenyu, and Tian Fangbao. Thu . "A Full-Newton Step Infeasible Interior-Point Algorithm for Linear Programming Based on a Kernel Function". United States. doi:10.1007/S00245-009-9069-X.
@article{osti_21241844,
title = {A Full-Newton Step Infeasible Interior-Point Algorithm for Linear Programming Based on a Kernel Function},
author = {Liu Zhongyi and Sun, Wenyu and Tian Fangbao},
abstractNote = {This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming, which is an extension of the work of Roos (SIAM J. Optim. 16(4):1110-1136, 2006). The main iteration of the algorithm consists of a feasibility step and several centrality steps. We introduce a kernel function in the algorithm to induce the feasibility step. For parameter p element of [0,1], the polynomial complexity can be proved and the result coincides with the best result for infeasible interior-point methods, that is, O(nlog n/{epsilon})},
doi = {10.1007/S00245-009-9069-X},
journal = {Applied Mathematics and Optimization},
number = 2,
volume = 60,
place = {United States},
year = {Thu Oct 15 00:00:00 EDT 2009},
month = {Thu Oct 15 00:00:00 EDT 2009}
}
  • The current project is a renewal of the PI`s previous projects supported by the Department of Energy. The original funding period for this project was from August 15, 1995 to August 14, 1996. The expiration date of the project was extended at no cost to August 14, 1997 in order to ensure a adequate completion of the original scope of work within the available funds. During this extended project period, the PI moved from the University of Maryland Baltimore County to Rice University. The primary objective of the project was to bring a successful conclusion to an effort of transferringmore » years of research into a freely available software package that are more accessible and user-friendly than then existing technologies in the field. Another objective of the project was to facilitate the transition of the PI`s research concentrations to other areas of practical importance: in particular, to the area of semidefinite programming where interior-point methodology has proven to be most promising. Both the objectives have been successfully accomplished. The software package LIPSOL, a centerpiece of the project, has recently been licensed to The MathWorks Inc. by the University of Maryland Baltimore County for planned incorporation into Matlab as the linear-program solver of Matlab. The PI has also made a number of contributions to the on-going research activities on semidefinite programming and other areas.« less
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