Interior-point methods and their applications to power systems: a classification of publications and software codes

Since Karmarkar's first successful interior-point algorithm for linear programming in 1984, the interest and consequently the number of publications in the area have increased tremendously, leaving the newcomers to the field trapped in a jungle of papers and reports. In this paper,the authors review and classify major publications on interior-point methods theory, on the practical implementation of the most successful interior-point algorithms, and on their applications to power systems optimization problems. A listing of state-of-the-art interior-point software codes and major online research resources on the Internet are included.

[1]  V. Quintana,et al.  A tutorial description of an interior point method and its applications to security-constrained economic dispatch , 1993 .

[2]  S. Granville.  Optimal reactive dispatch through interior point methods , 1994 .

[3]  Renato D. C. Monteiro,et al.  Interior path following primal-dual algorithms. part I: Linear programming , 1989, Math. Program..

[4]  John E. Mitchell,et al.  Computational Experience with an Interior Point Cutting Plane Algorithm , 1999, SIAM J. Optim..

[5]  V. R. Sherkat,et al.  Experience with interior point optimization software for a fuel planning application , 1993 .

[6]  John M. Mulvey,et al.  Higher-Order Predictor-Corrector Interior Point Methods with Application to Quadratic Objectives , 1993, SIAM J. Optim..

[7]  Antonio J. Conejo,et al.  A clipping-off interior-point technique for medium-term hydro-thermal coordination , 1999 .

[8]  J. Gondzio.  HOPDM (version 2.12) — A fast LP solver based on a primal-dual interior point method , 1995 .

[9]  Robert E. Bixby,et al.  Progress in Linear Programming , 1993 .

[10]  Barry W. Peyton,et al.  Block Sparse Cholesky Algorithms on Advanced Uniprocessor Computers , 1991, SIAM J. Sci. Comput..

[11]  Robert J. Vanderbei,et al.  Symmetric Quasidefinite Matrices , 1995, SIAM J. Optim..

[12]  G. L. Torres,et al.  An interior-point method for nonlinear optimal power flow using voltage rectangular coordinates , 1998 .

[13]  Roy E. Marsten,et al.  Numerical Factorization Methods for Interior Point Algorithms , 1994, INFORMS J. Comput..

[14]  Antonio J. Conejo,et al.  A new clipping-off interior-point algorithm to solve the medium-term hydro-thermal coordination problem , 1997, CCECE '97. Canadian Conference on Electrical and Computer Engineering. Engineering Innovation: Voyage of Discovery. Conference Proceedings.

[15]  Hiroshi Sasaki,et al.  A decoupled solution of hydro-thermal optimal power flow problem by means of interior point method and network programming , 1998 .

[16]  Michael A. Saunders,et al.  Inertia-Controlling Methods for General Quadratic Programming , 1991, SIAM Rev..

[17]  Fernando L. Alvarado,et al.  Weighted Least Absolute Value state estimation using interior point methods , 1994 .

[18]  Alan George,et al.  The Evolution of the Minimum Degree Ordering Algorithm , 1989, SIAM Rev..

[19]  Mauricio G. C. Resende,et al.  Data Structures and Programming Techniques for the Implementation of Karmarkar's Algorithm , 1989, INFORMS J. Comput..

[20]  R. Adapa,et al.  Economic operation and planning of multi-area interconnected power systems , 1995 .

[21]  Robert J. Vanderbei,et al.  ALPO: Another Linear Program Optimizer , 1993, INFORMS J. Comput..

[22]  Anoop Gupta,et al.  Efficient sparse matrix factorization on high performance workstations—exploiting the memory hierarchy , 1991, TOMS.

[23]  Joseph R. Shinnerl,et al.  Stability of Symmetric Ill-Conditioned Systems Arising in Interior Methods for Constrained Optimization , 1996, SIAM J. Matrix Anal. Appl..

[24]  J. Bunch,et al.  Decomposition of a symmetric matrix , 1976 .

[25]  Renato D. C. Monteiro,et al.  Interior path following primal-dual algorithms. part II: Convex quadratic programming , 1989, Math. Program..

[26]  T. Tsuchiya,et al.  On the formulation and theory of the Newton interior-point method for nonlinear programming , 1996 .

[27]  M. Aganagic,et al.  Long-term/mid-term resource optimization of a hydro-dominant power system using interior point method , 1995 .

[28]  Hua Wei,et al.  An interior point method for power system weighted nonlinear L/sub 1/ norm static state estimation , 1998 .

[29]  L. Khachiyan.  Polynomial algorithms in linear programming , 1980 .

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

[31]  Roy E. Marsten,et al.  Implementation of a Dual Affine Interior Point Algorithm for Linear Programming , 1989, INFORMS J. Comput..

[32]  J. Bunch,et al.  Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations , 1971 .

[33]  Chan-nan Lu,et al.  Network constrained security control using an interior point algorithm , 1993 .

[34]  Knud D. Andersen,et al.  The APOS linear programming solver: an implementation of the homogeneous algorithm , 1997 .

[35]  Margaret H. Wright,et al.  Interior methods for constrained optimization , 1992, Acta Numerica.

[36]  Erling D. Andersen,et al.  Presolving in linear programming , 1995, Math. Program..

[37]  Knud D. Andersen.  A modified Schur-complement method for handling dense columns in interior-point methods for linear programming , 1996, TOMS.

[38]  R. E. Marsten,et al.  A direct nonlinear predictor-corrector primal-dual interior point algorithm for optimal power flows , 1993 .

[39]  Sanjay Mehrotra,et al.  Solving symmetric indefinite systems in an interior-point method for linear programming , 1993, Math. Program..

[40]  Clyde L. Monma,et al.  An Implementation of a Primal-Dual Interior Point Method for Linear Programming , 1989, INFORMS J. Comput..

[41]  I. Lustig,et al.  Computational experience with a primal-dual interior point method for linear programming , 1991 .

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

[43]  Roy E. Marsten,et al.  Computational experience with a globally convergent primal—dual predictor—corrector algorithm for linear programming , 1994, Math. Program..

[44]  Mark T. Jones,et al.  An improved incomplete Cholesky factorization , 1995, TOMS.

[45]  Hua Wei,et al.  An interior point nonlinear programming for optimal power flow problems with a novel data structure , 1997 .

[46]  Joseph W. H. Liu,et al.  On Finding Supernodes for Sparse Matrix Computations , 1993, SIAM J. Matrix Anal. Appl..

[47]  R. Vanderbei.  Splitting dense columns in sparse linear systems , 1991 .

[48]  Mauricio G. C. Resende,et al.  An implementation of Karmarkar's algorithm for linear programming , 1989, Math. Program..

[49]  Eva K. Lee,et al.  COMPUTATIONAL EXPERIENCE OF AN INTERIOR-POINT SQP ALGORITHM IN A PARALLEL BRANCH-AND-BOUND FRAMEWORK , 2000 .

[50]  Jacek Gondzio,et al.  Multiple centrality corrections in a primal-dual method for linear programming , 1996, Comput. Optim. Appl..

[51]  Roy E. Marsten,et al.  On Implementing Mehrotra's Predictor-Corrector Interior-Point Method for Linear Programming , 1992, SIAM J. Optim..

[52]  G. Irisarri,et al.  Maximum loadability of power systems using interior point nonlinear optimization method , 1997 .

[53]  Michael A. Saunders,et al.  On projected newton barrier methods for linear programming and an equivalence to Karmarkar’s projective method , 1986, Math. Program..

[54]  V. Quintana,et al.  Improving an interior-point-based OPF by dynamic adjustments of step sizes and tolerances , 1999 .

[55]  Shinji Mizuno,et al.  A primal—dual affine-scaling potential-reduction algorithm for linear programming , 1993, Math. Program..

[56]  G. C. Ejebe,et al.  Preventive/corrective control for voltage stability using direct interior point method , 1997 .

[57]  Victor H. Quintana,et al.  An infeasible interior-point algorithm for optimal power-flow problems , 1996 .

[58]  J.C.O. Mello,et al.  The effects of voltage collapse problems in the reliability evaluation of composite systems , 1997 .

[59]  Anders Forsgren,et al.  Computing Modified Newton Directions Using a Partial Cholesky Factorization , 1995, SIAM J. Sci. Comput..

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

[61]  Michael A. Saunders,et al.  Primal—dual methods for linear programming , 1995, Math. Program..

[62]  Earl R. Barnes,et al.  A variation on Karmarkar’s algorithm for solving linear programming problems , 1986, Math. Program..

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

[64]  Hiroshi Yamashita,et al.  Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization , 1996, Math. Program..

[65]  Robert E. Bixby,et al.  Commentary - Progress in Linear Programming , 1994, INFORMS J. Comput..

[66]  S. Granville,et al.  Application of interior point methods to power flow unsolvability , 1996 .

[67]  Sanjay Mehrotra,et al.  Implementations of Affine Scaling Methods: Approximate Solutions of Systems of Linear Equations Using Preconditioned Conjugate Gradient Methods , 1992, INFORMS J. Comput..

[68]  Kumaraswamy Ponnambalam,et al.  A fast algorithm for power system optimization problems using an interior point method , 1991 .

[69]  K. D. Frey,et al.  Treatment of inequality constraints in power system state estimation , 1995 .

[70]  A. Bagchi,et al.  Economic dispatch with network and ramping constraints via interior point methods , 1998 .

[71]  Robert J. Vanderbei,et al.  Symmetric indefinite systems for interior point methods , 1993, Math. Program..

[72]  Robert J. Vanderbei,et al.  Commentary - Interior-Point Methods: Algorithms and Formulations , 1994, INFORMS J. Comput..

[73]  Michael A. Saunders,et al.  Preconditioners for Indefinite Systems Arising in Optimization , 1992, SIAM J. Matrix Anal. Appl..

[74]  Sanjay Mehrotra,et al.  On the Implementation of a Primal-Dual Interior Point Method , 1992, SIAM J. Optim..

[75]  Leon S. Lasdon,et al.  Primal-Dual and Primal Interior Point Algorithms for General Nonlinear Programs , 1995, INFORMS J. Comput..

[76]  R. Adapa,et al.  The quadratic interior point method solving power system optimization problems , 1994 .

[77]  H. Sasaki,et al.  An application of interior point quadratic programming algorithm to power system optimization problems , 1995 .

[78]  F. Alvarado,et al.  Constrained LAV state estimation using penalty functions , 1997 .

[79]  C. Mészáros.  On free variables in interior point methods , 1998 .

[80]  V. Quintana,et al.  An efficient predictor-corrector interior point algorithm for security-constrained economic dispatch , 1997 .

[81]  A.C.G. Melo,et al.  Simultaneous transfer capability assessment by combining interior point methods and Monte Carlo simulation , 1997 .

[82]  Antonio J. Conejo,et al.  A comparison of interior-point codes for medium-term hydro-thermal coordination , 1997 .