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The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems

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  • Le An
  • Pham Tao

Abstract

The DC programming and its DC algorithm (DCA) address the problem of minimizing a function f=g−h (with g,h being lower semicontinuous proper convex functions on R n ) on the whole space. Based on local optimality conditions and DC duality, DCA was successfully applied to a lot of different and various nondifferentiable nonconvex optimization problems to which it quite often gave global solutions and proved to be more robust and more efficient than related standard methods, especially in the large scale setting. The computational efficiency of DCA suggests to us a deeper and more complete study on DC programming, using the special class of DC programs (when either g or h is polyhedral convex) called polyhedral DC programs. The DC duality is investigated in an easier way, which is more convenient to the study of optimality conditions. New practical results on local optimality are presented. We emphasize regularization techniques in DC programming in order to construct suitable equivalent DC programs to nondifferentiable nonconvex optimization problems and new significant questions which have to be answered. A deeper insight into DCA is introduced which really sheds new light on DCA and could partly explain its efficiency. Finally DC models of real world nonconvex optimization are reported. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:133:y:2005:i:1:p:23-46:10.1007/s10479-004-5022-1
    DOI: 10.1007/s10479-004-5022-1
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    References listed on IDEAS

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    1. Le Thi, Hoai An & Pham, Dinh Tao & Thoai, Nguyen V., 2002. "Combination between global and local methods for solving an optimization problem over the efficient set," European Journal of Operational Research, Elsevier, vol. 142(2), pages 258-270, October.
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