Extension of convex models and its improvement on the approximate solution

In this paper, by means of combining non probabilistic convex modeling with perturbation theory, an improvement is made on the first order approximate solution in convex models of uncertainties. Convex modeling is extended to largely uncertain and non-convex sets of uncertainties and the combinational convex modeling is developed. The presented method not only extends applications of convex modeling, but also improves its accuracy in uncertain problems and computational efficiency. The numerical example illustrates the efficiency of the proposed method. The project supported by the National Outstanding Youth Science Foundation of China and the National Post Doctor Science Foundation of China