Generalized filtering algorithms for infeasibility analysis

We present generalized filtering algorithms for debugging linear, mixed integer and nonlinear infeasible programs. Given a set of constraints that are infeasible or inconsistent, we give algorithms to identify a minimal subset of these constraints that are inconsistent. The algorithms combine existing filtering algorithms with a binary-search based divide-and-conquer approach to improve search speed. We give computational results to show the speed of the algorithms on various problem types.

[1]  Said Salhi,et al.  Facility Location: A Survey of Applications and Methods , 1996 .

[2]  John W. Chinneck,et al.  Locating Minimal Infeasible Constraint Sets in Linear Programs , 1991, INFORMS J. Comput..

[3]  Erling D. Andersen.  On Primal and Dual Infeasibility Certificates in a Homogeneous Model for Convex Optimization , 2000, SIAM J. Optim..

[4]  John W. Chinneck,et al.  An effective polynomial-time heuristic for the minimum-cardinality IIS set-covering problem , 1996, Annals of Mathematics and Artificial Intelligence.

[5]  Mehrdad Tamiz,et al.  Detecting iis in infeasible linear programmes using techniques from goal programming , 1996, Comput. Oper. Res..

[6]  Donald Goldfarb,et al.  Second-order cone programming , 2003, Math. Program..

[7]  Stephen P. Boyd,et al.  Applications of second-order cone programming , 1998 .

[8]  Jennifer Ryan,et al.  Identifying Minimally Infeasible Subsystems of Inequalities , 1990, INFORMS J. Comput..

[9]  John W. Chinneck,et al.  Computer Codes for the Analysis of Infeasible Linear Programs , 1996 .

[10]  John W. Chinneck,et al.  Analyzing infeasible nonlinear programs , 1995, Comput. Optim. Appl..

[11]  L. Schrage.  Optimization Modeling With LINDO , 1997 .

[12]  Joyce van Loon.  Irreducibly inconsistent systems of linear inequalities , 1981 .

[13]  C. Floudas.  Handbook of Test Problems in Local and Global Optimization , 1999 .

[14]  John W. Chinneck,et al.  Analyzing Infeasible Mixed-Integer and Integer Linear Programs , 1999, INFORMS J. Comput..

[15]  John W. Chinneck,et al.  Finding a Useful Subset of Constraints for Analysis in an Infeasible Linear Program , 1997, INFORMS J. Comput..

[16]  Jorge J. Moré,et al.  Digital Object Identifier (DOI) 10.1007/s101070100263 , 2001 .