An Analyti Center Cutting Plane Method With Deep Cuts

An Analyti Center Cutting Plane Method

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...

Shallow, deep and very deep cuts in the analytic center cutting plane method

The analytic center cutting plane (ACCPM) methods aims to solve nondiieren-tiable convex problems. The technique consists of building an increasingly reened polyhedral approximation of the solution set. The linear inequalities that deene the approximation are generated by an oracle as hyperplanes separating a query point from the solution set. In ACCPM, the query point is the analytic center, o...

Multiple Cuts in the Analytic Center Cutting Plane Method

We analyze the multiple cut generation scheme in the analytic center cutting plane method. We propose an optimal primal and dual updating direction when the cuts are central. The direction is optimal in the sense that it maximizes the product of the new dual slacks and of the new primal variables within the trust regions defined by Dikin’s primal and dual ellipsoids. The new primal and dual dir...