A proximal cutting plane method using Chebychev center for nonsmooth convex optimization

A proximal cutting plane method using Chebychev center for nonsmooth convex optimization

An algorithm is developped for minimizing nonsmooth convex functions. This algortithm extends Elzinga-Moore cutting plane algorithm by enforcing the search of the next test point not too far from the previous ones, thus removing compactness assumption. Our method is to Elzinga-Moore’s algorithm what a proximal bundle method is to Kelley’s algorithm. As in proximal bundle methods, a quadratic pr...

Solving Nonlinear Multicommodity Flow Problems by the Proximal Chebychev Center Cutting Plane Algorithm

The recent algorithm proposed in [15] (called pcpa) for convex nonsmooth optimization, is specialized for applications in telecommunications on some nonlinear multicommodity flows problems. In this context, the objective function is additive and this property could be exploited for a better performance.

Convex Nondifferentiable Optimization: a Survey Focussed on the Analytic Center Cutting Plane Method

We present a survey of nondiierentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a self-contained convergence analysis, that uses the formalism of the theory of self-concordant functions, but for the main results, we give direct proofs based on the properties of the logarithmic function. We also provide an in depth analysis of ...

Convex nondifferentiable optimization: A survey focused on the analytic center cutting plane method

We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a self-contained convergence analysis, that uses the formalism of the theory of self-concordant functions, but for the main results, we give direct proofs based on the properties of the logarithmic function. We also provide an in depth analysis of...

Analytic Center Cutting-Plane Method