maratos effect – Optimization Online

Revisiting Superlinear Convergence of Proximal Newton-Like Methods to Degenerate Solutions

Published: 2026/02/11

Nonsmooth Optimization degenerate problems, error bound, maratos effect, proximal-Newton methods, regularized optimization, superlinear convergence

We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone operator. Superlinear convergence for both the distance to the solution set and a certain measure of first-order optimality … Read more

Global and Local Convergence of Line Search Filter Methods for Nonlinear Programming

Published: 2001/08/23, Updated: 2002/05/29

Lorenz T. Biegler

Andreas Wächter

Constrained Nonlinear Optimization barrier method, filter method, global convergence, interior point methods, line-search, local convergence, maratos effect, nonconvex constrained optimization, nonlinear programming, second order correction, sequential quadratic programming

Line search methods for nonlinear programming using Fletcher and Leyffer’s filter method, which replaces the traditional merit function, are proposed and their global and local convergence properties are analyzed. Previous theoretical work on filter methods has considered trust region algorithms and only the question of global convergence. The presented framework is applied to barrier interior … Read more