The theory of convex risk functions has now been well established as the basis for identifying families that should be used in risk-averse optimization problems. Despite its theoretical appeal, implementation a function remains difficult, because there is little guidance regarding how chosen so it also represents decision maker’s subjective preference. In this paper, we address issue through le...

Constrained optimization problems have a wide range of applications in science, economics, and engineering. In this paper, a neural network model is proposed to solve a class of nonsmooth constrained optimization problems with a nonsmooth convex objective function subject to nonlinear inequality and affine equality constraints. It is a one-layer non-penalty recurrent neural network based on the...

We consider the problem of portfolio selection, with transaction costs and constraints on exposure to risk. Linear transaction costs, bounds on the variance of the return, and bounds on different shortfall probabilities are efficiently handled by convex optimization methods. Problems with transaction costs that include a fixed fee, or discount breakpoints, cannot be directly solved by convex op...

Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. As direct rank minimization is NP hard, many alternative choices have been proposed. In this survey, we first introduce optimization approaches for two popular methods on rank minimization, i.e., nuclear norm regularization and rank constraint. Nuclear norm is the tightest con...