Copositivity meets D. C. optimization

<p style='text-indent:20px;'>Based on a work by M. Dur and J.-B. Hiriart-Urruty[<xref ref-type="bibr" rid="b3">3</xref>], we consider the problem of whether a symmetric matrix is copositive formulated as a difference of convex functions problem. The convex nondifferentiable function in this d.c. decomposition being proximable, we then apply a proximal-gradient method to approximate the related stationary points. Whereas, in [<xref ref-type="bibr" rid="b3">3</xref>], the DCA algorithm was used.</p>

On an algorithm in nondifferential convex optimization

In this paper an algorithm for minimization of a nondifferentiable function is presented. The algorithm uses the Moreau-Yosida regularization of the objective function and its second order Dini upper directional derivative. The purpose of the paper is to establish general hypotheses for this algorithm, under which convergence occurs to optimal points. A convergence proof is given, as well as an estimate of the rate of the convergence.

A trust region method using subgradient for minimizing a nondifferentiable function

The minimization of a particular nondifferentiable function is considered. The first and second order necessary conditions are given. A trust region method for minimization of this form of the objective function is presented. The algorithm uses the subgradient instead of the gradient. It is proved that the sequence of points generated by the algorithm has an accumulation point which satisfies the first and second order necessary conditions.