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Globally convergent DC trust-region methods

Author

Listed:
  • Hoai Le Thi
  • Van Huynh
  • Tao Dinh
  • A. Vaz
  • L. Vicente

Abstract

In this paper, we investigate the use of DC (Difference of Convex functions) models and algorithms in the application of trust-region methods to the solution of a class of nonlinear optimization problems where the constrained set is closed and convex (and, from a practical point of view, where projecting onto the feasible region is computationally affordable). 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 to first-order stationary points. The theory requires the use of exact second-order derivatives but, in turn, the computation of the trust-region step asks only for one projection onto the feasible region (in comparison to the calculation of the generalized Cauchy point which may require more). 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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Hoai Le Thi & Van Huynh & Tao Dinh & A. Vaz & L. Vicente, 2014. "Globally convergent DC trust-region methods," Journal of Global Optimization, Springer, vol. 59(2), pages 209-225, July.
    • Handle: RePEc:spr:jglopt:v:59:y:2014:i:2:p:209-225
    DOI: 10.1007/s10898-014-0170-6
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    References listed on IDEAS

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    1. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    2. A. Schwartz & E. Polak, 1997. "Family of Projected Descent Methods for Optimization Problems with Simple Bounds," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 1-31, January.
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