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Volume 21, Issue 4
Proximal Point Algorithm for Minimization of DC Function

Wen-Yu Sun, Raimundo J. B. de Sampaio & M. A. B. Candido

J. Comp. Math., 21 (2003), pp. 451-462.

Published online: 2003-08

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  • Abstract

In this paper we present some algorithms for minimization of DC function (difference of two convex functions). They are descent methods of the proximal-type which use the convex properties of the two convex functions separately. We also consider an approximate proximal point algorithm. Some properties of the $\epsilon$-subdifferential and the $\epsilon$-directional derivative are discussed. The convergence properties of the algorithms are established in both exact and approximate forms. Finally, we give some applications to the concave programming and maximum eigenvalue problems.

  • Keywords

Nonconvex optimization, Nonsmooth optimization, DC function, Proximal point algorithm, $\epsilon$-subgradient.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

raimundo.sampaio@pucpr.br (Raimundo J. B. de Sampaio)

  • BibTex
  • RIS
  • TXT
@Article{JCM-21-451, author = {Sun , Wen-YuJ. B. de Sampaio , Raimundo and Candido , M. A. B.}, title = {Proximal Point Algorithm for Minimization of DC Function}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {4}, pages = {451--462}, abstract = {

In this paper we present some algorithms for minimization of DC function (difference of two convex functions). They are descent methods of the proximal-type which use the convex properties of the two convex functions separately. We also consider an approximate proximal point algorithm. Some properties of the $\epsilon$-subdifferential and the $\epsilon$-directional derivative are discussed. The convergence properties of the algorithms are established in both exact and approximate forms. Finally, we give some applications to the concave programming and maximum eigenvalue problems.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10248.html} }
TY - JOUR T1 - Proximal Point Algorithm for Minimization of DC Function AU - Sun , Wen-Yu AU - J. B. de Sampaio , Raimundo AU - Candido , M. A. B. JO - Journal of Computational Mathematics VL - 4 SP - 451 EP - 462 PY - 2003 DA - 2003/08 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10248.html KW - Nonconvex optimization, Nonsmooth optimization, DC function, Proximal point algorithm, $\epsilon$-subgradient. AB -

In this paper we present some algorithms for minimization of DC function (difference of two convex functions). They are descent methods of the proximal-type which use the convex properties of the two convex functions separately. We also consider an approximate proximal point algorithm. Some properties of the $\epsilon$-subdifferential and the $\epsilon$-directional derivative are discussed. The convergence properties of the algorithms are established in both exact and approximate forms. Finally, we give some applications to the concave programming and maximum eigenvalue problems.

Sun , Wen-YuJ. B. de Sampaio , Raimundo and Candido , M. A. B.. (2003). Proximal Point Algorithm for Minimization of DC Function. Journal of Computational Mathematics. 21 (4). 451-462. doi:
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