Active set expansion strategies in MPRGP algorithm

02/14/2020
by   J. Kruzik, et al.
0

The paper investigates strategies for expansion of active set that can be employed by the MPRGP algorithm. The standard MPRGP expansion uses a projected line search in the free gradient direction with a fixed step length. Such a scheme is often too slow to identify the active set, requiring a large number of expansions. We propose to use adaptive step lengths based on the current gradient, which guarantees the decrease of the unconstrained cost function with different gradient-based search directions. Moreover, we also propose expanding the active set by projecting the optimal step for the unconstrained minimization. Numerical experiments demonstrate the benefits of our expansion step modifications on two benchmarks – contact problem of linear elasticity solved by TFETI and machine learning problems of SVM type, both implemented in PERMON toolbox.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/27/2022

On a discrete scheme for the Mullins-Sekerka flow and its fine properties

The Mullins-Sekerka problem is numerically solved in ℝ^2 with the aid of...
research
06/15/2023

MinMax Networks

While much progress has been achieved over the last decades in neuro-ins...
research
05/17/2023

Stochastic Ratios Tracking Algorithm for Large Scale Machine Learning Problems

Many machine learning applications and tasks rely on the stochastic grad...
research
04/17/2022

A Modified Nonlinear Conjugate Gradient Algorithm for Functions with Non-Lipschitz Gradient

In this paper, we propose a modified nonlinear conjugate gradient (NCG) ...
research
10/12/2021

Regularized Step Directions in Conjugate Gradient Minimization for Machine Learning

Conjugate gradient minimization methods (CGM) and their accelerated vari...
research
10/03/2020

Learning the Step-size Policy for the Limited-Memory Broyden-Fletcher-Goldfarb-Shanno Algorithm

We consider the problem of how to learn a step-size policy for the Limit...

Please sign up or login with your details

Forgot password? Click here to reset