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Proximal point algorithm for minimization of DC function. (English) Zbl 1107.90427
Summary: 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 $$\varepsilon$$-subdifferential and the $$\varepsilon$$-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.

##### MSC:
 90C26 Nonconvex programming, global optimization 49J52 Nonsmooth analysis 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming