A new infeasible interior-point algorithm with full step for linear optimization based on a simple function

In this paper, we design and analyse an infeasible interior-point algorithm based on a simple function for linear optimization. The infeasible algorithm contains two types of search directions: the feasibility search direction and the centrality search direction. Both of the directions are determined by the simple function. The algorithm uses full step, thus no need to perform the line-search procedure. Although the proposed function is simple, as it will be shown, the induced infeasible algorithm enjoys the best-known iteration complexity for infeasible interior-point algorithm.

[1]  Kees Roos,et al.  A New Efficient Large-Update Primal-Dual Interior-Point Method Based on a Finite Barrier , 2002, SIAM J. Optim..

[2]  Hossein Mansouri,et al.  Improved Full-Newton Step O(nL) Infeasible Interior-Point Method for Linear Optimization , 2010 .

[3]  Jiming Peng,et al.  A Predictor-Corrector Algorithm for Linear Optimization Based on a Specific Self-Regular Proximity Function , 2005, SIAM J. Optim..

[4]  Fang Wu,et al.  On quadratic convergence of the $$O\left( {\sqrt {nL} } \right)$$ -iteration homogeneous and self‐duallinear programming algorithm , 1999, Ann. Oper. Res..

[5]  H. Mansouri.  Full-Newton step interior-point methods for conic optimization , 2008 .

[6]  Jiming Peng,et al.  New Complexity Analysis of the Primal—Dual Newton Method for Linear Optimization , 2000, Ann. Oper. Res..

[7]  Stephen J. Wright.  Primal-Dual Interior-Point Methods , 1997, Other Titles in Applied Mathematics.

[8]  Jean-Philippe Vial,et al.  Theory and algorithms for linear optimization - an interior point approach , 1998, Wiley-Interscience series in discrete mathematics and optimization.

[9]  G. Gu.  Full-step interior-point methods for symmetric optimization , 2009 .

[10]  Kees Roos,et al.  A Full-Newton Step O(n) Infeasible Interior-Point Algorithm for Linear Optimization , 2006, SIAM J. Optim..

[11]  Kunio Tanabe,et al.  Centered newton method for mathematical programming , 1988 .

[12]  C. Roos,et al.  An Infeasible Interior-Point Algorithm with full-Newton Step for Linear Optimization , 2008 .

[13]  Irvin Lustig,et al.  Feasibility issues in a primal-dual interior-point method for linear programming , 1990, Math. Program..

[14]  M. El Ghami,et al.  New Primal-dual Interior-point Methods Based on Kernel Functions , 2005 .

[15]  Hossein Mansouri,et al.  A new full-Newton step O(n) infeasible interior-point algorithm for semidefinite optimization , 2009, Numerical Algorithms.

[16]  Shinji Mizuno,et al.  A primal—dual infeasible-interior-point algorithm for linear programming , 1993, Math. Program..

[17]  Shinji Mizuno,et al.  An O(√nL)-Iteration Homogeneous and Self-Dual Linear Programming Algorithm , 1994, Math. Oper. Res..

[18]  Hossein Mansouri,et al.  An adaptive infeasible interior-point algorithm with full-Newton step for linear optimization , 2013 .

[19]  C. Roos,et al.  A New and Efficient Large-Update Interior-Point Method for Linear Optimization , 2001 .

[20]  Jiming Peng,et al.  Self-regular functions and new search directions for linear and semidefinite optimization , 2002, Math. Program..

[21]  Shinji Mizuno,et al.  Polynomiality of infeasible-interior-point algorithms for linear programming , 1994, Math. Program..

[22]  Yin Zhang,et al.  On the Convergence of a Class of Infeasible Interior-Point Methods for the Horizontal Linear Complementarity Problem , 1994, SIAM J. Optim..

[23]  Guoqing Zhang,et al.  McMaster University Advanced Optimization Laboratory Title : The Complexity of Self-Regular Proximity Based Infeasible , 2003 .

[24]  Wenyu Sun,et al.  A Full-Newton Step Infeasible Interior-Point Algorithm for Linear Programming Based on a Kernel Function , 2009 .

[25]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, Comb..

[26]  Kees Roos,et al.  A Comparative Study of Kernel Functions for Primal-Dual Interior-Point Algorithms in Linear Optimization , 2004, SIAM J. Optim..

[27]  Kees Roos,et al.  A primal‐dual interior-point method for linear optimization based on a new proximity function , 2002, Optim. Methods Softw..

[28]  Yinyu Ye,et al.  Interior point algorithms: theory and analysis , 1997 .

[29]  Jiming Peng,et al.  Self-regularity - a new paradigm for primal-dual interior-point algorithms , 2002, Princeton series in applied mathematics.