In this paper we establish necessary as well as sufficient conditions for a given feasible point to be a global minimizer of smooth minimization problems with mixed variables. These problems, for instance, cover box constrained smooth minimization problems and bivalent optimization problems. In particular, our results provide necessary global optimality conditions for difference convex minimiza...

where f ,g :Rn →R are convex continuous functions and S is a nonempty, convex compact in Rn. Such problems have many practical and theoretical applications in telecommunication, mechanics, engineering design, economics, and other fields (see [1, 2, 21], etc.) and have been studied actively over the last four decades (see, e.g., [9, 19] and their references). In addition to these direct applicat...

We combine a systematic approach for deriving general posteriori error estimates convex minimization problems based on duality relations with recently derived generalized Marini formula. The are quasi constant-free and apply to large class of variational including the <mml:semantics...

The Newton Bracketing method [9] for the minimization of convex functions f : Rn → R is extended to affinely constrained convex minimization problems. The results are illustrated for affinely constrained Fermat–Weber location problems.

We show how certain nonconvex optimization problems that arise in image processing and computer vision can be restated as convex minimization problems. This allows, in particular, the finding of global minimizers via standard convex minimization schemes.

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...