A reformulation–linearization–convexification algorithm for optimal correction of an inconsistent system of linear constraints

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.