Alternative DC Algorithm for Partial DC programming

In this paper, we introduce an alternative DC algorithm for solving partial DC programs. This proposed algorithm is an natural extension of the standard DC algorithm. Furthermore, we also consider an inexact version of this alternative DC algorithm. The convergence of these proposed algorithms (both the exact and inexact versions) are investigated. The applications to … Read more

Characterizations of Differentiability, Smoothing Techniques and DC Programming with Applications to Image Reconstructions

In this paper, we study characterizations of differentiability for real-valued functions based on generalized differentiation. These characterizations provide the mathematical foundation for Nesterov’s smoothing techniques in infinite dimensions. As an application, we provide a simple approach to image reconstructions based on Nesterov’s smoothing techniques and DC programming that involves the $\ell_1-\ell_2$ regularization. Article Download View … Read more

A branch and bound approach for convex semi-infinite programming

In this paper we propose an efficient approach for globally solving a class of convex semi-infinite programming (SIP) problems. Under the objective function and constraints (w.r.t. the variables to be optimized) convexity assumption, and appropriate differentiability, we propose a branch and bound exchange type method for SIP. To compute a feasible point for a SIP … Read more

Globally convergent DC trust-region methods

In this paper, we investigate the use of DC (Difference of Convex functions) models and algorithms in the solution of nonlinear optimization problems by trust-region methods. We consider DC local models for the quadratic model of the objective function used to compute the trust-region step, and apply a primal-dual subgradient method to the solution of … Read more