line search algorithm – Optimization Online

A linearly convergent algorithm for variational inequalities based on fiber bundle

Published: 2025/09/27, Updated: 2025/11/20

Complementarity and Variational Inequalities, Game Theory fiber bundle, interior point method, line search algorithm, variational inequality problem

The variational inequality (VI) problem is a fundamental mathematical framework for many classical problems. This paper introduces an algorithm that applies to arbitrary finite-dimensional VIs with general compact convex sets and general continuous functions. The algorithm guarantees global linear convergence to an approximate solution without requiring any assumptions, including the typical monotonicity. Our approach adapts … Read more

On the use of the energy norm in trust-region and adaptive cubic regularization subproblems

Published: 2017/04/26

Elhoucine Bergou

Youssef Diouane

Serge Gratton

Unconstrained Optimization adaptive regularized framework using cubics, conjugate gradient method, energy norm, krylov subspace methods, line search algorithm, nonlinear optimization, trust-region methods, unconstrained optimization

We consider solving unconstrained optimization problems by means of two popular globalization techniques: trust-region (TR) algorithms and adaptive regularized framework using cubics (ARC). Both techniques require the solution of a so-called “subproblem” in which a trial step is computed by solving an optimization problem involving an approximation of the objective function, called “the model”. The … Read more