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 - <p style="text-align: justify;">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.</p>