analytic center – Page 2 – Optimization Online

Multiple Cuts with a Homogeneous Analytic Center Cutting Plane Method

Published: 2001/05/25

Convex Optimization analytic center, conic formulation, cutting planes, multiple cuts

This paper analyzes the introduction of multiple central cuts in a conic formulation of the analytic center cutting plane method (in short ACCPM). This work extends earlier work on the homogeneous ACCPM, and parallels the analysis of the multiple cut process in the standard ACCPM. The main issue is the calculation of a direction that … Read more

A BFGS-IP algorithm for solving strongly convex optimization problems with feasibility enforced by an exact penalty approach

Published: 2001/02/01

Paul Armand

Jean Charles Gilbert

Sophie Jan-Jégou

Constrained Nonlinear Optimization analytic center, bfgs quasi-newton approximations, constrained optimization, convex optimization, infeasible iterates, interior point methods, line-search, primal-dual algorithms, shift and slack variables, superlinear convergence

This paper introduces and analyses a new algorithm for minimizing a convex function subject to a finite number of convex inequality constraints. It is assumed that the Lagrangian of the problem is strongly convex. The algorithm combines interior point methods for dealing with the inequality constraints and quasi-Newton techniques for accelerating the convergence. Feasibility of … Read more