Interior point methods : current status and future directions

This article provides a synopsis of the major developments in interior point methods for mathematical programming in the last thirteen years, and discusses current and future research directions in interior point methods, with a brief selective guide to the research literature.1

[1]  A. Tucker,et al.  Linear Inequalities And Related Systems , 1956 .

[2]  Elmer Earl. Branstetter,et al.  The theory of linear programming , 1963 .

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

[4]  Nimrod Megiddo,et al.  A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems , 1991, Lecture Notes in Computer Science.

[5]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[6]  Clóvis C. Gonzaga,et al.  Path-Following Methods for Linear Programming , 1992, SIAM Rev..

[7]  Shinji Mizuno,et al.  A General Framework of Continuation Methods for Complementarity Problems , 1993, Math. Oper. Res..

[8]  Roy E. Marsten,et al.  Feature Article - Interior Point Methods for Linear Programming: Computational State of the Art , 1994, INFORMS J. Comput..

[9]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[10]  Dick den Hertog,et al.  Interior Point Approach to Linear, Quadratic and Convex Programming: Algorithms and Complexity , 1994 .

[11]  Yurii Nesterov,et al.  Interior-point polynomial algorithms in convex programming , 1994, Siam studies in applied mathematics.

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

[13]  R. Saigal Linear Programming: A Modern Integrated Analysis , 1995 .

[14]  B. Jansen,et al.  A Short Survey on Ten Years Interior Point Methods , 1995 .

[15]  James Renegar,et al.  Linear programming, complexity theory and elementary functional analysis , 1995, Math. Program..

[16]  Farid Alizadeh,et al.  Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization , 1995, SIAM J. Optim..

[17]  Michael J. Todd,et al.  Potential-reduction methods in mathematical programming , 1997, Math. Program..

[18]  Jacek Gondzio,et al.  Implementation of Interior Point Methods for Large Scale Linear Programming , 1996 .

[19]  Yinyu Ye,et al.  A simplified homogeneous and self-dual linear programming algorithm and its implementation , 1996, Ann. Oper. Res..

[20]  Takashi Tsuchiya,et al.  Affine Scaling Algorithm , 1996 .

[21]  Yinyu Ye,et al.  A primal-dual interior point method whose running time depends only on the constraint matrix , 1996, Math. Program..

[22]  Shinji Mizuno,et al.  Infeasible-Interior-Point Algorithms , 1996 .

[23]  Osman Güler,et al.  Barrier Functions in Interior Point Methods , 1996, Math. Oper. Res..

[24]  Yinyu Ye,et al.  How Partial Knowledge Helps to Solve Linear Programs , 1996, J. Complex..

[25]  K. M. Anstreicher,et al.  Interior point methods in mathematical programming , 1996 .

[26]  Xihui Yan Infeasible primal-dual interior point algorithms for solving optimal power flow problems , 1997 .

[27]  John N. Tsitsiklis,et al.  Introduction to linear optimization , 1997, Athena scientific optimization and computation series.

[28]  T Talaky,et al.  Interior Point Methods of Mathematical Programming , 1997 .

[29]  Michael L. Overton,et al.  Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results , 1998, SIAM J. Optim..

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

[31]  Robert J. Vanderbei,et al.  Linear Programming: Foundations and Extensions , 1998, Kluwer international series in operations research and management service.

[32]  E. Yaz Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

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

[34]  Robert M. Freund,et al.  Condition measures and properties of the central trajectory of a linear program , 1998, Math. Program..