Smoothing Conservative Approximation For Constrained Optimization Of Fuzzy Relation

In this paper,we investigate the solution of constrained programming problem of fuzzy relation inequality with addition-min composition.This kind of problem is non-smooth,and there are some smoothing methods to solve it.However,most of the existing algorithms are based on non-conservative approximations,so the feasibility of the approximate solution cannot be guaranteed.In this paper,a new smoothing approximation of the constraint is constructed by using a deformation of sigmoid function,and then a new smoothing approximation algorithm is constructed.It is proved that any cluster point of the solution sequence generated by the new algorithm is an optimal solution of the original problem.At the same time,the convergence of the optimal value is obtained,and the effectiveness of the algorithm is obtained theoretically.At the same time,the numerical experiments show that the new algorithm has obvious advantages in feasibility compared with the existing algorithms,and the advantages will be magnified with the increase of dimension.With respect to calculation accuracy and calculation speed,there is not much difference from the existing algorithm.