SIPAMPL: Semi-infinite programming with AMPL

SIPAMPL is an environment for coding semi-infinite programming (SIP) problems. This environment includes a database containing a set of SIP problems that have been collected from the literature and a set of routines. It allows users to code their own SIP problems in AMPL, to use any problem already in the database, and to develop and test any SIP solver. The SIPAMPL routines support the interface between a potential SIP solver and test problems coded in AMPL. SIPAMPL also provides a tool that allows the selection of problems from the database with specified characteristics. As a concept demonstration, we show how MATLAB can use SIPAMPL to solve the problems in the database. The Linux and Microsoft Windows versions together with the database of coded problems are freely available via the web.

[1]  Teresa León,et al.  On the numerical treatment of linearly constrained semi-infinite optimization problems , 2000, Eur. J. Oper. Res..

[2]  Alexander Potchinkov.  Design of optimal linear phase FIR filters by a semi-infinite programming technique , 1997, Signal Process..

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

[4]  R. Reemtsen,et al.  Discretization methods for the solution of semi-infinite programming problems , 1991 .

[5]  Georg Still,et al.  Discretization in semi-infinite programming: the rate of convergence , 2001, Math. Program..

[6]  Adrian S. Lewis,et al.  An extension of the simplex algorithm for semi-infinite linear programming , 1989, Math. Program..

[7]  Brian W. Kernighan,et al.  The C Programming Language , 1978 .

[8]  A. Tits,et al.  A globally convergent algorithm with adaptively refined discretization for semi-infinite optimization problems arising in engineering design , 1989 .

[9]  S. Marin.  Optimal parametrization of curves for robot trajectory design , 1988 .

[10]  S. Fang,et al.  A semi-infinite programming model for earliness/tardiness production planning with a genetic algorithm , 1996 .

[11]  Elke Haaren-Retagne.  A semi-infinite programming algorithm for robot trajectory planning , 1992 .

[12]  S. Fang,et al.  An inexact approach to solving linear semi-infinite programming problems , 1994 .

[13]  Teresa León,et al.  A multi-local optimization algorithm , 1998 .

[14]  Michael C. Ferris,et al.  An interior point algorithm for semi-infinite linear programming , 1989, Math. Program..

[15]  Michael J. Todd,et al.  Interior-point algorithms for semi-infinite programming , 1994, Math. Program..

[16]  Yoshihiro Tanaka,et al.  A trust region method for semi-infinite programming problems , 1999, Int. J. Syst. Sci..

[17]  Rainer Hettich,et al.  An implementation of a discretization method for semi-infinite programming , 1986, Math. Program..

[18]  Kok Lay Teo,et al.  A dual parameterization approach to linear-quadratic semi-infinite programming problems , 1999 .

[19]  C. J. Price,et al.  Non-linear semi-infinite programming , 1992 .

[20]  Mark S. Gockenbach,et al.  Optimal Signal Sets for Non-Gaussian Detectors , 1999, SIAM J. Optim..

[21]  Yongli Li,et al.  A semi-infinite programming model for earliness/tardiness production planning with simulated annealing , 1997 .

[22]  Bjarne Stroustrup,et al.  C++ Programming Language , 1986, IEEE Softw..

[23]  André L. Tits,et al.  An SQP Algorithm for Finely Discretized Continuous Minimax Problems and Other Minimax Problems with Many Objective Functions , 1996, SIAM J. Optim..

[24]  C. Goh,et al.  A simple computational procedure for optimization problems with functional inequality constraints , 1987 .

[25]  R. Hettich.  A comparison of some numerical methods for semi-infinite programming , 1979 .

[26]  C. J. Price,et al.  Numerical experiments in semi-infinite programming , 1996, Comput. Optim. Appl..

[27]  C. C. Gonzaga,et al.  An improved algorithm for optimization problems with functional inequality constraints , 1980 .

[28]  A. Tits,et al.  Feasible Sequential Quadratic Programming for Finely Discretized Problems from SIP , 1998 .

[29]  Rainer Hettich,et al.  A note on an implementation of a method for quadratic semi-infinite programming , 1990, Math. Program..

[30]  Kok Lay Teo,et al.  A new computational algorithm for functional inequality constrained optimization problems , 1993, Autom..

[31]  Chih-Jen Lin,et al.  An Unconstrained Convex Programming Approach to Linear Semi-Infinite Programming , 1998, SIAM J. Optim..

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

[33]  Kok Lay Teo,et al.  A computational algorithm for functional inequality constrained optimization problems , 1990, Autom..

[34]  J. E. Falk,et al.  Infinitely constrained optimization problems , 1976 .

[35]  G. A. Watson,et al.  Numerical Experiments with Globally Convergent Methods for Semi-Infinite Programming Problems , 1983 .

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

[37]  Kenneth O. Kortanek,et al.  A Central Cutting Plane Algorithm for Convex Semi-Infinite Programming Problems , 1993, SIAM J. Optim..

[38]  Defeng Sun,et al.  First-Order Algorithms for Generalized Semi-Infinite Min-Max Problems , 1999, Comput. Optim. Appl..

[39]  G. Alistair Watson,et al.  A projected lagrangian algorithm for semi-infinite programming , 1985, Math. Program..