Assessing the Potential of Interior Methods for Nonlinear Optimization

A series of numerical experiments with interior point (LOQO, KNITRO) and active-set sequential quadratic programming (SNOPT, filterSQP) codes are reported and analyzed. The tests were performed with small, medium-size and moderately large problems, and are examined by problem classes. Detailed observations on the performance of the codes, and several suggestions on how to improve them are presented. Overall, interior methods appear to be strong competitors of act ive-set SQP methods, but all codes show much room for improvement.

[1]  T. Steihaug.  The Conjugate Gradient Method and Trust Regions in Large Scale Optimization , 1983 .

[2]  Lamberto Cesari,et al.  Optimization-Theory And Applications , 1983 .

[3]  E. Omojokun.  Trust region algorithms for optimization with nonlinear equality and inequality constraints , 1990 .

[4]  P. Toint,et al.  Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A) , 1992 .

[5]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[6]  Arne Stolbjerg Drud,et al.  CONOPT - A Large-Scale GRG Code , 1994, INFORMS J. Comput..

[7]  Nicholas I. M. Gould,et al.  CUTE: constrained and unconstrained testing environment , 1995, TOMS.

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

[9]  Jorge Nocedal,et al.  On the Local Behavior of an Interior Point Method for Nonlinear Programming , 1997 .

[10]  Michael L. Overton,et al.  A Primal-dual Interior Method for Nonconvex Nonlinear Programming , 1998 .

[11]  Peter Spellucci,et al.  A new technique for inconsistent QP problems in the SQP method , 1998, Math. Methods Oper. Res..

[12]  Jorge J. Moré,et al.  The NEOS Server , 1998 .

[13]  Anders Forsgren,et al.  Primal-Dual Interior Methods for Nonconvex Nonlinear Programming , 1998, SIAM J. Optim..

[14]  Robert J. Vanderbei,et al.  An Interior-Point Algorithm for Nonconvex Nonlinear Programming , 1999, Comput. Optim. Appl..

[15]  Jorge Nocedal,et al.  An Interior Point Algorithm for Large-Scale Nonlinear Programming , 1999, SIAM J. Optim..

[16]  P. Armand,et al.  A Feasible BFGS Interior Point Algorithm for Solving Strongly Convex Minimization Problems , 1999 .

[17]  Paul Armand,et al.  A Feasible BFGS Interior Point Algorithm for Solving Convex Minimization Problems , 2000, SIAM J. Optim..

[18]  Robert J. Vanderbei,et al.  Interior-point methods for nonconvex nonlinear programming: orderings and higher-order methods , 2000, Math. Program..

[19]  Jorge Nocedal,et al.  A trust region method based on interior point techniques for nonlinear programming , 2000, Math. Program..

[20]  Nicholas I. M. Gould,et al.  A primal-dual trust-region algorithm for non-convex nonlinear programming , 2000, Math. Program..

[21]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[22]  Jorge J. Moré,et al.  Benchmarking optimization software with COPS. , 2001 .

[23]  Sven Leyffer,et al.  Nonlinear programming without a penalty function , 2002, Math. Program..

[24]  Jorge J. Moré,et al.  Benchmarking optimization software with performance profiles , 2001, Math. Program..

[25]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2002, SIAM J. Optim..

[26]  José Luis Morales,et al.  A numerical study of limited memory BFGS methods , 2002, Appl. Math. Lett..

[27]  Nicholas I. M. Gould,et al.  Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming , 2002, SIAM J. Optim..

[28]  Hiroshi Yamashita,et al.  A globally and superlinearly convergent primal-dual interior point trust region method for large scale constrained optimization , 2005, Math. Program..