conjugate directions – Optimization Online

A modified limited-memory BNS method for unconstrained minimization based on the conjugate directions idea

Published: 2014/03/12

A modification of the limited-memory variable metric BNS method for large scale unconstrained optimization is proposed, which consist in corrections (derived from the idea of conjugate directions) of the used difference vectors for better satisfaction of previous quasi-Newton conditions. In comparison with [16], where a similar approach is used, correction vectors from more previous iterations … Read more

Modifications of the limited-memory BNS method for better satisfaction of previous quasi-Newton conditions

Published: 2011/12/16

Ladislav Lukšan

Jan Vlček

Nonlinear Optimization, Unconstrained Optimization conjugate directions, limited-memory methods, preliminary numerical results, the bfgs update, unconstrained optimization, variable metric methods

Several modifications of the limited-memory variable metric BNS method for large scale unconstrained optimization are proposed, which consist in corrections (derived from the idea of conjugate directions) of the used di®erence vectors to improve satisfaction of previous quasi-Newton conditions, utilizing information from previous or subsequent iterations. In case of quadratic objective functions, conjugacy of all … Read more

A conjugate directions approach to improve the limited-memory BFGS method

Published: 2011/08/08

Ladislav Lukšan

Jan Vlček

Nonlinear Optimization, Unconstrained Optimization conjugate directions, limited-memory methods, numerical results, the bfgs update, unconstrained optimization, variable metric methods

Simple modifiations of the limited-memory BFGS method (L-BFGS) for large scale unconstrained optimization are considered, which consist in corrections (derived from the idea of conjugate directions) of the used difference vectors, utilizing information from the preceding iteration. In case of quadratic objective functions, the improvement of convergence is the best one in some sense and … Read more

A nonmonotone truncated Newton-Krylov method exploiting negative curvature directions, for large scale unconstrained optimization: complete results

Published: 2008/09/04

Giovanni Fasano

Stefano Lucidi

Unconstrained Optimization conjugate directions, negative curvatures, nonmonotone stabilization technique, second order necessary conditions, truncated newton methods

We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions: the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative … Read more