951 research outputs found
An optimal subgradient algorithm for large-scale convex optimization in simple domains
This paper shows that the optimal subgradient algorithm, OSGA, proposed in
\cite{NeuO} can be used for solving structured large-scale convex constrained
optimization problems. Only first-order information is required, and the
optimal complexity bounds for both smooth and nonsmooth problems are attained.
More specifically, we consider two classes of problems: (i) a convex objective
with a simple closed convex domain, where the orthogonal projection on this
feasible domain is efficiently available; (ii) a convex objective with a simple
convex functional constraint. If we equip OSGA with an appropriate
prox-function, the OSGA subproblem can be solved either in a closed form or by
a simple iterative scheme, which is especially important for large-scale
problems. We report numerical results for some applications to show the
efficiency of the proposed scheme. A software package implementing OSGA for
above domains is available
On the convergence of a linesearch based proximal-gradient method for nonconvex optimization
We consider a variable metric linesearch based proximal gradient method for
the minimization of the sum of a smooth, possibly nonconvex function plus a
convex, possibly nonsmooth term. We prove convergence of this iterative
algorithm to a critical point if the objective function satisfies the
Kurdyka-Lojasiewicz property at each point of its domain, under the assumption
that a limit point exists. The proposed method is applied to a wide collection
of image processing problems and our numerical tests show that our algorithm
results to be flexible, robust and competitive when compared to recently
proposed approaches able to address the optimization problems arising in the
considered applications
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