We consider the `1-regularized least-squares problem for sparse recovery and compressed sensing. Since the objective function is not strongly convex, standard proximal gradient methods only achieve sublinear convergence. We propose a homotopy continuation strategy, which employs a proximal gradient method to solve the problem with a sequence of decreasing regularization parameters. It is shown ...

In the theory of optimization an essential role is played by the differentiability of convex functions. In this paper we shall try to extend the results concerning differentiability to a larger class of functions called strongly α(·)-paraconvex. Let (X, ‖.‖) be a real Banach space. Let f(x) be a real valued strongly α(·)-paraconvex function defined on an open convex subset Ω ⊂ X , i.e. f ( tx+(...

In this paper a proximal point algorithm for convex function is considered in complete CAT(0) spaces. We introduce necessary and sufficient condition the set of minimizers to be nonempty, by showing that case, iterative sequence converges strongly metric projection some onto function.

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.

Abstract Let f be analytic in the unit disk $${\mathbb {D}}=\{z\in {\mathbb {C}}:|z|&lt;1 \}$$ D = { z ∈ C : | &lt; 1 } </mml:mat...