In this paper, we consider a wide class of constrained nonconvex regularized minimization problems, where the constraints are linearly constraints. It was reported in the literature that nonconvex regularization usually yields a solution with more desirable sparse structural properties beyond convex ones. However, it is not easy to obtain the proximal mapping associated with nonconvex regulariz...

This paper presents a comprehensive review and some new developments on canonical duality theory for nonconvex systems. Based on a tri-canonical form for quadratic minimization problems, an insightful relation between canonical dual transformations and nonlinear (or extended) Lagrange multiplier methods is presented. Connections between complementary variational principles in nonconvex mechanic...

Automatic control systems, electronic circuit design, image registration, SLAM and several other engineering problems all require nonconvex optimization. Many approaches have been developed to carry out such nonconvex optimization, but they suffer drawbacks including large computation time, require tuning of multiple unintuitive parameters and are unable to find multiple local/global minima. In...

The use of convex regularizers allow for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones. However, the resultant optimization problem is much harder. In this paper, for a large class of nonconvex regularizers, we propose to move the nonconvexity fro...

What is the relation between notion of Nash equilibria and Pareto-optimal points? It well known that do not need to be Pareto optimal, points equilibria. However, paper “Characterizing Computing Set Equilibria via Vector Optimization” by Feinstein Rudloff takes a deeper look at relation. shown it possible characterize set all as solutions certain vector optimization problem. This accomplished c...