constrained optimization – Page 7

Feasible Interior Methods Using Slacks for Nonlinear Optimization

Published: 2001/02/12

A slack-based feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modified so that the … 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