A Novel Smoothing Approach for Linear Objective Optimizations Subject to Fuzzy Relation Inequalities With Addition-Min Composition

This article mainly investigates a smoothing approach for solving linear objective optimizations subject to fuzzy relational inequalities with addition-min composition. Since their constraints are concave, it is almost impossible to convert such a problem into a linear programming, which has a convex feasible domain. In this article, we construct a second-order continuously differentiable function for smoothing the constraints. Based on the approximation, a new smoothing approach is proposed for solving the problem. It is proved that any cluster of the generated solution sequence is an optimal solution. The convergence of optimal values is also proved. Some numerical experiments are presented for illustrating the performance and the effectiveness of the new approach. The numerical results show that, compared to the given smoothing method, the new approach usually reaches a more accurate solution both in sense of feasibility and optimality.