A global regularization method for solving the finite min-max problem

Computational Optimization and Applications

Volumn 11, Issue 3, 1998, Pages 277-295

  Barrientos, O ^a  

^a Subgerencia Planificacion Nac   (Chile)

Author keywords

Min max; Nondifferentiable optimization; Quasi Newton methods; Regularization technique

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; FUNCTION EVALUATION; MATHEMATICAL OPERATORS; OPTIMIZATION; TECHNOLOGY;

MIN-MAX; NONDIFFERENTIABLE OPTIMIZATION; QUASI-NEWTON METHODS; REGULARIZATION TECHNIQUE;

PROBLEM SOLVING;

EID: 0002250023     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1018601319372     Document Type: Article

References (14)

1. H. Attouch and R.J.B. Wets, "Approximation and convergence in non-linear optimization," in Nonlinear Programming, O. Mangasarian, R.R. Meyer, and S.M. Robinson (Eds.), Academic Press: New York, pp. 367-394, 1980.
2. C. Charalambous and A.R. Conn, "An efficient method to solve the minmax problem directly," SIAM J. Numer. Anal., vol. 15, pp. 162-187, 1978.
3. F.H. Clarke, "Generalized gradients and applications," Trans. Amer. Math. Soc., vol. 205, pp. 247-262, 1975.
4. V.F. Demyanov and V.N. Malozemov, "On the theory of non-linear min-max problems," Russian Math. Surveys, vol. 26, pp. 57-115, 1971.
5. C. Gígola and S. Gómez, "A regularization method for solving the finite convex min-max problem," SIAM J. Numer. Anal., vol. 27, pp. 1621-1634, 1990.
6. S.P. Han, "Variable metric methods for minimizing a class of non-differentiable functions," Math. Programming, vol. 20, pp. 1-13, 1981.
7. J.B. Hiriart-Urruty and C. Lemaréchal, "Convex analysis and minimization algorithms," Grundlehren der Mathematischen Wissenschaften, vol. 305, Springer-Verlag: New York, 1993.
8. C. Lemaréchal and R. Mifflin (Eds.), Nonsmooth Optimization: Proceedings of a IIASA Workshop 1977 Laxenburg, IIASA Proceedings Series, vol. 3, Pergamon Press: Oxford, 1978.
9. B. Martinet, "Régularisation d'inéquations variationnelles par approximations succesives," Rev. Française Inf. Rech. Oper., vol. R-3, pp. 154-179, 1970.
10. M. Minoux, Programmation Mathématique: Théorie et Algorithmes, Dunod: Paris, 1983.
11. W. Murray and M.L. Overton, "A projective Lagrange algorithm for nonlinear min-max optimization," SIAM J. Sci. Statist. Comput., vol. 1, pp. 345-370, 1980.
12. R.T. Rockafellar, Convex Analysis, Princeton University Press: Princeton, NJ, 1970.
13. R.T. Rockafellar, "Monotone operators and proximal point algorithm," SIAM J. Control and Optimization, vol. 14, pp. 877-898, 1976.
14. I. Zang, "A smoothing-out technique for min-max optimization," Math. Programming, vol. 19, pp. 61-77, 1980.