matrix-free methods – Optimization Online

Adaptive Augmented Lagrangian Methods: Algorithms and Practical Numerical Experience

Published: 2014/08/19, Updated: 2017/01/02

In this paper, we consider augmented Lagrangian (AL) algorithms for solving large-scale nonlinear optimization problems that execute adaptive strategies for updating the penalty parameter. Our work is motivated by the recently proposed adaptive AL trust region method by Curtis et al. [An adaptive augmented Lagrangian method for large-scale constrained optimization, Math. Program. 152 (2015), pp.201–245.]. … Read more

An Adaptive Augmented Lagrangian Method for Large-Scale Constrained Optimization

Published: 2012/12/17, Updated: 2017/01/02

Frank E. Curtis

Daniel P. Robinson

Hao Jiang

Nonlinear Optimization augmented lagrangian method, large-scale optimization, matrix-free methods, nonconvex optimization, nonlinear optimization, steering methods

We propose an augmented Lagrangian algorithm for solving large-scale constrained optimization problems. The novel feature of the algorithm is an adaptive update for the penalty parameter motivated by recently proposed techniques for exact penalty methods. This adaptive updating scheme greatly improves the overall performance of the algorithm without sacrificing the strengths of the core augmented … Read more

Convergence Analysis of an Inexact Feasible Interior Point Method for Convex Quadratic Programming

Published: 2012/08/29

Jacek Gondzio

Linear, Cone and Semidefinite Programming inexact newton method, interior point methods, linear programming, matrix-free methods, quadratic programming, worst-case complexity analysis

In this paper we will discuss two variants of an inexact feasible interior point algorithm for convex quadratic programming. We will consider two different neighbourhoods: a (small) one induced by the use of the Euclidean norm which yields a short-step algorithm and a symmetric one induced by the use of the infinity norm which yields … Read more