Random perturbation of the variable metric method for unconstrained nonsmooth nonconvex optimization

International Journal of Applied Mathematics and Computer Science

Volumn 16, Issue 4, 2006, Pages 463-474

  El Mouatasim, Abdelkrim ^a   Ellaia, Rachid ^a   Souza de Cursi, José E ^b  

^a MOHAMMED V UNIVERSITY   (Morocco)

^b CNRS   (France)

Author keywords

Generalized gradient; Nonconvex optimization; Nonsmooth optimization; Stochastic perturbation; Variable metric method

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; PERTURBATION TECHNIQUES; RANDOM PROCESSES;

GENERALIZED GRADIENT; NONCONVEX OPTIMIZATION; NONSMOOTH OPTIMIZATION; STOCHASTIC PERTURBATION; VARIABLE METRIC METHOD;

OPTIMIZATION;

EID: 33846269345     PISSN: 1641876X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (35)

1. Aluffi-Pentini F., Parisi V. and Zirilli F. (1988): ALGORITHM 667. SIGMA -A Stochastic-Integration Global Minimization Algorithm. - ACM Trans. Math. Softw., Vol. 14, No. 4, pp. 366-380.
2. Bagirov A.M., Rubinov A.M., Soukhoroukova N.V. and Yearwood J. (2003): Unsupervised and supervised data classification via nonsmooth and global optimization. - Trab. Invest. Oper., Vol. 11, No. 1, pp. 1-93.
3. Batukhtin V.D., Kirillova F.M. and Ukhobotov V.I. (1998): Nonsmooth and discontinuous problems of control and optimization. - Proc. IFAC Workshop NDPCO'98, Chelyabinsk, Russia, pp. 25-34.
4. Bihain A. (1984): Optimization of upper semidifferentiable functions. - J. Optim. Theory Applic., Vol. 4, No. 4, pp. 545-568.
5. Bouleau N. (1986): Variables Aléatoires et Simulation. - Paris: Editions Hermann.
6. Boyd S., Xiao L. and Mutapcic A. (2003): Subgradient Methods. - Notes for EE392o, Stanford University.
7. Carson Y. and Maria A. (1997): Simulation optimization: Methods and applications. - Proc. Winter Simulation Conf., Atlanta, GA, USA, pp. 118-126.
8. Clarke F. (1983): Optimization and Nonsmooth Analysis. - New York: Wiley.
9. Clarke F. (1975): Generalized gradient and applications. - Trans. Amer. Math. Soc., Vol. 205, pp. 247-262.
10. Davidon W. (1991): Variable metric method for minimization. - SIAM J. Optim., Vol. 1, No. 1, pp. 1-17.
11. Dorea C.C.Y. (1990): Stopping rules for a random optimization method. - SIAM J. Contr. Optim., Vol. 28, No. 4, pp. 841-850.
12. Ellaia R. (1992): Contributions à l'optimisation globale et à l'analyse nondifférentiable. - Thèse d'état, Université Mohammed V, Faculté des Sciences, Rabat, Morocco.
13. Ellaia R. and Elmouatasim. A., (2004): Random perturbation of reduced gradient method for global optimization. - Proc. Conf. Modelling, Computation and Optimization, MCO'04, Metz, France, (to appear.)
14. Fletcher R. (1980): Practical Methods of Optimization, Vol. 2. - New York: Wiley.
15. Hiriart-Urruty J. and Lemaréchal C. (1993): Convex Analysis and Minimization Algorithms II. - Berlin: Springer.
16. Kiwiel K.C. (1985): Method of Descent for Nondifferentiable Optimization. - Berlin: Springer.
17. Kiwiel K.C. (1989): An ellipsoid trust region bundle method for nonsmooth convex minimization. - SIAM J. Contr. Optim., Vol. 27, No. 4, pp. 737-757.
18. Kiwiel K.C. (1994): Free-steering relaxation methods for problems with strictly convex costs and linear constraints. - Tech. Rep. IIASA, No. A-2361, Laxenburg, Austria.
19. Larsson T., Patrksson M. and Stromberg A.B. (1996): Conditional subgradient optimization - Theory and applications. - Europ. J. Oper. Res., Vol. 88, No. 2, pp. 382-403.
20. Lemaréchal C. (1982): Numerical experiments in nonsmooth optimization. - Proc. IIASA Workshop Progress in Nondifferentiable Optimization, Laxemburg, Austria, pp. 61-84.
21. Lemaréchal C., Strodiot J.J. and Bibain A. (1981): On a bundle algorithm for nonsmooth optimization, In: Nonlinear Programming 4 (O. Mangasarian, R. Meyer and S. Robinson, Eds.). - New York: Academic Press, pp. 245-282.
22. Makela M.M. and Neinaanmaki P. (1992): Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control. - London: World Scientific.
23. Nguyen V.H. and Strodiot J.J. (1992): Computing a Global Optimal Solution to a Design Centering Problem. - Tech. Rep., No. 88/12, Facultés Universitaires Notre-Dame de la Paix, Belgium.
24. Outrata J. (1987): On numerical solution of optimal control problems with nonsmooth objectives: Application to economic models. - Kybernetika, Vol. 23, pp. 54-66.
25. Outrata J., Kocvara M. and Zowe J. (1998): Nonsmooth Approach to Optimization Problems Oita with Equilibrium Constraints: Theory, Applications & Numerical Results. - Dordrecht: Kluwer.
26. Pierre L. and Renée T (1996): On the Deng-Lin random number generators and related methods, In: Global Optimization in Action (Pinter J., Ed.). - Les cahiers; du GERAD, Dordrecht: Kluwer.
27. Pogu M. and Souza J.E. (1994): Global optimization by random perturbation of the gradient method with a fixed parameter. - J. Glob. Optim., Vol. 5, No. 2, pp. 159-180.
28. Schramm H. and Zowe J. (1992): A version of the bundle idea for minimizing a nonsmooth function: Conceptual idea, convergence analysis, numerical results. - SIAM J. Optim., Vol. 2, No. 1, pp. 121-152.
29. Souza de Cursi J.E. (1992a): Minimisation stochastique de fonctionnelles non convexes en dimension finie. - Tech. Rep. ECN, Available at http:// meca.insa-rouen.fr/-souza
30. Souza de Cursi J.E. (1992b): Recuit simulé et application à l'approximation par des sommes d'exponentielles.- Tech. Rep. ECN, Available at http://meca.insa-rouen.fr/-souza
31. Souza de Cursi J.E., Ellaia R. and Boubadi M. (2003): Global optimization under nonlinear restrictions by using stochastic perturbations of the projected gradient, In: Frontiers In Global Optimization (C.A. Floudas and Panos Pardalos, Eds.). - Boston, MA: Kluwer Academic Publishers, Nonconvex Optim. Appl., Vol. 74, pp. 541-561.
32. Souza de Cursi J.E., Ellaia R. and El Mouatasim A. (2005): Stochastic perturbation of active set method for nonconvex nonsmooth optimization problem with linear constraints. - RAIRO-Recherche Operational, (submitted).
33. Uryasev S.P. (1991): New variable metric algorithms for non-differentiable optimization problems. - J. Optim. Theory Applic., Vol. 71, No. 2, pp. 359-388.
34. Wang I.J. and Spall J.C. (1999): A constrained simultaneous perturbation stochastic approximation algorithm based on penalty functions. - Proc. Amer. Contr. Conf. San Diego, CA, Vol. 1, pp. 393-399.
35. Zowe J. (1985): Nondifferentiable optimization, In: Computational Mathematical Programming (K. Schittkowski, Ed.). - Berlin: Springer Verlag, pp. 323-356.