Dominique Orban – Page 3 – Optimization Online

Componentwise fast convergence in the solution of full-rank systems of nonlinear equations

Published: 2001/06/11, Updated: 2002/02/25

Constrained Nonlinear Optimization, Nonlinear Systems and Least-Squares componentwise q-superlinear convergence, nonlinear systems of equations, path-following methods

The asymptotic convergence of parameterized variants of Newton’s method for the solution of nonlinear systems of equations is considered. The original system is perturbed by a term involving the variables and a scalar parameter which is driven to zero as the iteration proceeds. The exact local solutions to the perturbed systems then form a differentiable … Read more

Properties of the Log-Barrier Function on Degenerate Nonlinear Programs

Published: 2001/06/01, Updated: 2003/05/29

Dominique Orban

Stephen Wright

Constrained Nonlinear Optimization degenerate programs, interior point methods, mangasarian and fromovitz constraint qualification, strict complementarity

We examine the sequence of local minimizers of the log-barrier function for a nonlinear program near a solution at which second-order sufficient conditions and the Mangasarian-Fromovitz constraint qualifications are satisfied, but the active constraint gradients are not necessarily linearly independent. When a strict complementarity condition is satisfied, we show uniqueness of the local minimizer of … Read more