A “thermal” perceptron learning rule
Neural Computation
The complexity and approximability of finding maximum feasible subsystems of linear relations
Theoretical Computer Science
On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The MIN PFS problem and piecewise linear model estimation
Discrete Applied Mathematics - Special issue: Third ALIO-EURO meeting on applied combinatorial optimization
Fast Heuristics for the Maximum Feasible Subsystem Problem
INFORMS Journal on Computing
Large-scale linear programming techniques for the design of protein folding potentials
Mathematical Programming: Series A and B
Linearity Embedded in Nonconvex Programs
Journal of Global Optimization
Randomized relaxation methods for the maximum feasible subsystem problem
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
On the approximability of the maximum feasible subsystem problem with 0/1-coefficients
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A relaxable service selection algorithm for QoS-based web service composition
Information and Software Technology
Approximating infeasible 2VPI-systems
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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We consider the maximum feasible subsystem problem in which, given an infeasible system of linear inequalities, one wishes to determine a largest feasible subsystem. The focus is on the version with bounded variables that naturally arises in several fields of application. To tackle this NP-hard problem, we propose a simple but efficient two-phase relaxation-based heuristic. First a feasible subsystem is derived from a relaxation (linearization) of an exact continuous bilinear formulation, and then a smaller subproblem is solved to optimality in order to identify all other inequalities that can be added to the current feasible subsystem while preserving feasibility. Computational results, reported for several classes of instances, arising from classification and telecommunication applications, indicate that our method compares well with one of the best available heuristics and with state-of-the-art exact algorithms.