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Globally convergent DC trust-region methods

Le Thi Hoai An(hoai-an.le-thi***at***univ-lorraine.fr)
Huynh Van Ngai(hoai-an.le-thi***at***univ-lorraine.fr)
Pham Dinh Tao(pham***at***insa- rouen.fr)
A. I. F. Vaz(aivaz***at***dps.uminho.pt)
L. N. Vicente(lnv***at***mat.uc.pt)

Abstract: In this paper, we investigate the use of DC (Difference of Convex functions) models and algorithms in the solution of nonlinear optimization problems by trust-region methods. We consider DC local models for the quadratic model of the objective function used to compute the trust-region step, and apply a primal-dual subgradient method to the solution of the corresponding trust-region subproblems. One is able to prove that the resulting scheme is globally convergent for first-order stationary points. The theory requires the use of exact second-order derivatives but, in turn, requires a minimum from the solution of the trust-region subproblems for problems where projecting onto the feasible region is computationally affordable. In fact, only one projection onto the feasible region is required in the computation of the trust-region step which seems in general less expensive than the calculation of the generalized Cauchy point. The numerical efficiency and robustness of the proposed new scheme when applied to bound-constrained problems is measured by comparing its performance against some of the current state-of-the-art nonlinear programming solvers on a vast collection of test problems.

Keywords: Trust-region methods, DC algorithm, global convergence, bound constraints.

Category 1: Nonlinear Optimization

Category 2: Global Optimization

Citation: Preprint 13-09, Dept. Mathematics, Univ. Coimbra.

Download: [PDF]

Entry Submitted: 04/23/2013
Entry Accepted: 04/23/2013
Entry Last Modified: 04/23/2013

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