Discrete gradient method: Derivative-free method for nonsmooth optimization

Journal of Optimization Theory and Applications

Volumn 137, Issue 2, 2008, Pages 317-334

  Bagirov, A M ^a   Karasozen B ^b   Sezer, M ^b  

^a Centre for Informatics and Applied Optimization   (Australia)

^b MIDDLE EAST TECHNICAL UNIVERSITY   (Turkey)

Author keywords

Derivative free optimization; Discrete gradients; Nonsmooth optimization; Subdifferentials

Indexed keywords

GRADIENT METHODS; OPTIMIZATION;

DERIVATIVE-FREE METHODS; DERIVATIVE-FREE OPTIMIZATION; DISCRETE GRADIENT; DISCRETE GRADIENT METHOD; NON-SMOOTH FUNCTIONS; NONSMOOTH OPTIMIZATION; NONSMOOTH OPTIMIZATION PROBLEMS; OPTIMIZATION SOLVERS; SUBDIFFERENTIALS; UNCONSTRAINED NONSMOOTH OPTIMIZATION;

NUMERICAL METHODS;

EID: 42449163031     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-007-9335-5     Document Type: Article

References (25)

1. Frangioni, A.: Generalized bundle methods. SIAM J. Optim. 113, 117-156 (2002)
2. Gaudioso, M., Monaco, M.F.: A bundle type approach to the unconstrained minimization of convex nonsmooth functions. Math. Program. 23, 216-226 (1982)
3. Hiriart-Urruty, J.B., Lemarechal, C.: Convex Analysis and Minimization Algorithms, vols. 1 and 2. Springer, Heidelberg (1993)
4. Kiwiel, K.C.: Methods of Descent for Nondifferentiable Optimization. Lecture Notes in Mathematics, vol. 1133. Springer, Berlin (1985)
5. Lemarechal, C.: An extension of Davidon methods to nondifferentiable problems. In: Balinski, M.L., Wolfe, P. (eds.) Nondifferentiable Optimization. Mathematical Programming Study, vol. 3, pp. 95-109. North-Holland, Amsterdam (1975)
6. Mifflin, R.: An algorithm for constrained optimization with semismooth functions. Math. Oper. Res. 2, 191-207 (1977)
7. Zowe, J.: Nondifferentiable optimization: A motivation and a short introduction into the subgradient and the bundle concept. In: Schittkowski, K. (ed.) Computational Mathematical Programming. NATO SAI Series, vol. 15, pp. 323-356. Springer, New York (1985)
8. Wolfe, P.H.: A method of conjugate subgradients of minimizing nondifferentiable convex functions. Math. Program. Study 3, 145-173 (1975)
9. Polak, E., Royset, J.O.: Algorithms for finite and semi-infinite min-max-min problems using adaptive smoothing techniques. J. Optim. Theory Appl. 119, 421-457 (2003)
10. Burke, J.V., Lewis, A.S., Overton, M.L.: A robust gradient sampling algorithm for nonsmooth, nonconvex optimization. SIAM J. Optim. 15, 751-779 (2005)
11. Audet, C., Dennis, J.E. Jr.: Analysis of generalized pattern searches. SIAM J. Optim. 13, 889-903 (2003)
12. Torzcon, V.: On the convergence of pattern search algorithms. SIAM J. Optim. 7, 1-25 (1997)
13. Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)
14. Mifflin, R.: Semismooth and semiconvex functions in constrained optimization. SIAM J. Control Optim. 15, 959-972 (1977)
15. Demyanov, V.F., Rubinov, A.M.: Constructive Nonsmooth Analysis. Peter Lang, Frankfurt am Main (1995)
16. Bagirov, A.M., Rubinov, A.M., Soukhoroukova, A.V., Yearwood, J.: Supervised and unsupervised data classification via nonsmooth and global optimisation. TOP: Spanish Oper. Res. J. 11, 1-93 (2003)
17. Bagirov, A.M., Yearwood, J.: A new nonsmooth optimisation algorithm for minimum sum-of-squares clustering problems. Eur. J. Oper. Res. 170, 578-596 (2006)
18. Bagirov, A.M.: Minimization methods for one class of nonsmooth functions and calculation of semi-equilibrium prices. In: Eberhard, A., et al. (eds.) Progress in Optimization: Contribution from Australasia, pp. 147-175. Kluwer Academic, Dordrecht (1999)
19. Bagirov, A.M.: Continuous subdifferential approximations and their applications. J. Math. Sci. 115, 2567-2609 (2003)
20. Wolfe, P.H.: Finding the nearest point in a polytope. Math. Program. 11, 128-149 (1976)
21. Frangioni, A.: Solving semidefinite quadratic problems within nonsmooth optimization algorithms. Comput. Oper. Res. 23, 1099-1118 (1996)
22. Kiwiel, K.C.: A dual method for certain positive semidefinite quadratic programming problems. SIAM J. Sci. Stat. Comput. 10, 175-186 (1989)
23. Luks̃an, L., Vlc̃ek, J.: Test problems for nonsmooth unconstrained and linearly constrained optimization. Technical Report 78, Institute of Computer Science, Academy of Sciences of the Czech Republic (2000)
24. GAMS: The solver manuals. GAMS Development Corporation, Washington D.C. (2004)
25. Bergen, F.V.: CONDOR: a constrained, non-linear, derivative-free parallel optimizer for continuous, high computing load, noisy objective functions. Ph.D. thesis, Université Libre de Bruxelles, Belgium (2004)