Variable Metric Forward-Backward Algorithm for Composite Minimization Problems

A block coordinate variable metric forward-backward algorithm

A number of recent works have emphasized the prominent role played by the KurdykaLojasiewicz inequality for proving the convergence of iterative algorithms solving possibly nonsmooth/nonconvex optimization problems. In this work, we consider the minimization of an objective function satisfying this property, which is a sum of a non necessarily convex differentiable function and a non necessaril...

Variable Metric Method for Minimization

A Combined Variable Metric - Conjugate Gradient Algorithm for a Class of Large Scale Unconstrained Minimization Problems

An algorithm is being presented for a special class of unconstrained minimization problems. The algorithm exploits the special structure of the Hessian in the problems under consideration, It is based on applying Bertsekas' I-1] Scaled Partial Conjugate Gradient method with respect to a metric that is updated by the Rank One update, using gradients obtained in the preceeding steps. Two classes ...

Variable Metric Forward-Backward Algorithm for Minimizing the Sum of a Differentiable Function and a Convex Function

We consider the minimization of a function G defined on R , which is the sum of a (non necessarily convex) differentiable function and a (non necessarily differentiable) convex function. Moreover, we assume that G satisfies the KurdykaLojasiewicz property. Such a problem can be solved with the Forward-Backward algorithm. However, the latter algorithm may suffer from slow convergence. We propose...

A Particle Swarm Optimization Algorithm for Mixed-Variable Nonlinear Problems

Many engineering design problems involve a combination of both continuous anddiscrete variables. However, the number of studies scarcely exceeds a few on mixed-variableproblems. In this research Particle Swarm Optimization (PSO) algorithm is employed to solve mixedvariablenonlinear problems. PSO is an efficient method of dealing with nonlinear and non-convexoptimization problems. In this paper,...