Proximal point algorithm for minimization of DC function

Journal of Computational Mathematics

Volumn 21, Issue 4, 2003, Pages 451-462

  Sun, Wen Yu ^a   Sampaio, Raimundo J B ^b   Candido, M A B ^b  

^a NANJING NORMAL UNIVERSITY   (China)

^b PONTIFICAL CATHOLIC UNIVERSITY OF PARANÁ   (Brazil)

Author keywords

subgradient; DC function; Nonconvex optimization; Nonsmooth optimization; Proximal point algorithm

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS;

DC FUNCTION; NONCONVEX OPTIMIZATION; NONSMOOTH OPTIMIZATION; PROXIMAL POINT ALGORITHM;

APPROXIMATION THEORY;

EID: 0142261105     PISSN: 02549409     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. G. Auchmuty, Duality algorithm for nonconvex variational principle, Research Report UH/MD-41, University of Houston, (1988).
2. F.H. Clarke, Optimization and Nonsmooth Analysis, John Wiley and Sons, New York, (1983).
3. E. Fernandez-Cara and C. Moreno, Critical points approximation through exact regularization, Mathematics of Computation, 50 (1988) 139-153.
4. M. Fukushima, A descent algorithm for nonsmooth convex optimization, Mathematical Programming, 30 (1984), 163-175.
5. M. Fukushima and L. Qi, A globally and superlinearly convergent algorithm for nonsmooth convex minimization, SIAM J. Optimization, 6 (1996), 1106-1120.
6. J.B. Hiriart-Urruty, From convex optimization to nonconvex optimization, necessary and sufficient conditions for global optimization, Nonsmooth Optimization and Related Topics, Plenum Press, (1989), 219-240.
7. J.B. Hiriart-Urruty, Generalized differenciability, duality and optimization for problems dealing with difference of convex functions, Convexity and Duality in Optimization, Lecture Notes in Economics And Mathematical Systems 256, (1986), 37-70.
8. J.B. Hiriart-Urruty and H. Tuy, Essays on nonconvex optimization, Mathematical Programming, 41 (1988).
9. J.B. Hiriart-Urruty and C. Lemarechal, Convex Analysis and Minimization Algorithms II, Sringer-Verlag, Berlin, (1993).
10. K.C. Kiwiel, Proximity control in bundle methods for convex non-differentiable minimization, Mathematical Programming, 46 (1990), 105-122.
11. H. Mine and M. Fukushima, A minimization method for the sum of a convex function and a continuously different table function, J. Optimization Theory and Applications, 33 (1981), 9-23.
12. J.S. Pang and L. Qi, Nonsmooth equations: motivation and algorithms, SIAM J. Optimization, 3 (1993), 443-465.
13. D.T. Pham and E.B. Souad, Algorithms for solving a class of nonconvex optimizations problems: methods of subgradient, Fermat Days 85: Mathematics for Optimization, North Holland, (1986).
14. L. Qi, Convergence analysis of some algorithms for solving nonsmooth equations, Mathematics of Operations Research, 18 (1993), 227-244.
15. L. Qi and W. Sun, An iterative method for minimax problem, in D.Z. Du and P.M. Pardalos eds., Minimax and Applications, (Kluwer Academic Publisher, New York, 1995), 55-67.
16. R.T. Rockafellar, Convex Analysis, Princeton University Press, (1970).
17. R.T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control and Optimization, 14 (1976), 877-898.
18. R.T. Rockafellar and R.J.-B. Wets, Variational Analysis, Springer-Verlag, New York, (1997).
19. R.J.B. Sampaio, Contribution to study of dc programming, Doctoral Thesis, Catholic University of Rio de Janeiro, (1990).
20. R.J.B. Sampaio, W. Sun and J. Yuan, On trust region algorithm for nonsmooth optimization, Applied Mathematics and Computation, 85 (1997), 109-116.
21. W. Sun, On convergence of an iterative method for minimax problem, J. Australian Mathematics Society, Series B, 39 (1997), 280-292.
22. 1 constrained optimization, Applied Mathematics and Computation, 92 (1998), 69-84.
23. J.F. Toland, Duality in nonconvex optimization, J. of Mathematical Analysis and Applications, 66 (1978), 399-415.
24. Y. Yuan and W. Sun, Optimization Theory and Methods, Science Press, Beijing, 1997.
25. W.I. Zangwill, Nonlinear Programming: A Unified Approach, Prentice-Hall, 1969.