Enhancements of ANALYZE: a computer-assisted analysis system for linear programming
ACM Transactions on Mathematical Software (TOMS)
MINOS(IIS): infeasibility analysis using MINOS
Computers and Operations Research
Some perturbation theory for linear programming
Mathematical Programming: Series A and B
The complexity and approximability of finding maximum feasible subsystems of linear relations
Theoretical Computer Science
Ill-Posedness and the Complexity of Deciding Existence of Solutionsto Linear Programs
SIAM Journal on Optimization
Understanding the Geometry of Infeasible Perturbations of a Conic Linear System
SIAM Journal on Optimization
On Optimal Correction of Inconsistent Linear Constraints
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Analyzing Infeasible Mixed-Integer and Integer Linear Programs
INFORMS Journal on Computing
A review of recent advances in global optimization
Journal of Global Optimization
On optimal zero-preserving corrections for inconsistent linear systems
Journal of Global Optimization
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In this paper, an algorithm is introduced to find an optimal solution for an optimization problem that arises in total least squares with inequality constraints, and in the correction of infeasible linear systems of inequalities. The stated problem is a nonconvex program with a special structure that allows the use of a reformulation-linearization-convexification technique for its solution. A branch-and-bound method for finding a global optimum for this problem is introduced based on this technique. Some computational experiments are included to highlight the efficacy of the proposed methodology. Inconsistent systems play a major role on the reformulation of models and are a consequence of lack of communication between decision makers. The problem of finding an optimal correction for some measure is of crucial importance in this context. The use of the Frobenius norm as a measure seems to be quite natural and leads to a nonconvex fractional programming problem. Despite being a difficult global optimization, it is possible to process it by using a branch-and-bound algorithm incorporating a local nonlinear programming method.