Alexis Montoison – Optimization Online

MadNCL: A GPU Implementation of Algorithm NCL for Large-Scale, Degenerate Nonlinear Programs

Published: 2025/10/07

Constrained Nonlinear Optimization, Nonlinear Optimization

We present a GPU implementation of Algorithm NCL, an augmented Lagrangian method for solving large-scale and degenerate nonlinear programs. Although interior-point methods and sequential quadratic programming are widely used for solving nonlinear programs, the augmented Lagrangian method is known to offer superior robustness against constraint degeneracies and can rapidly detect infeasibility. We introduce several enhancements … Read more

BiLQ: An Iterative Method for Nonsymmetric Linear Systems with a Quasi-Minimum Error Property

Published: 2019/10/06

Alexis Montoison

Dominique Orban

Other Topics adjoint systems, integral functional, iterative methods, lanczos biorthogonalization process, least-norm subproblems, multiprecision, quasi-minimal error method, tridiagonalization process

We introduce an iterative method named BiLQ for solving general square linear systems Ax = b based on the Lanczos biorthogonalization process defined by least-norm subproblems, and is a natural companion to BiCG and QMR. Whereas the BiCG (Fletcher, 1976), CGS (Sonneveld, 1989) and BiCGSTAB (van der Vorst, 1992) iterates may not exist when the … Read more