Discrete Gradient Method: Derivative-Free Method for Nonsmooth Optimization
- 714 Downloads
A new derivative-free method is developed for solving unconstrained nonsmooth optimization problems. This method is based on the notion of a discrete gradient. It is demonstrated that the discrete gradients can be used to approximate subgradients of a broad class of nonsmooth functions. It is also shown that the discrete gradients can be applied to find descent directions of nonsmooth functions. The preliminary results of numerical experiments with unconstrained nonsmooth optimization problems as well as the comparison of the proposed method with the nonsmooth optimization solver DNLP from CONOPT-GAMS and the derivative-free optimization solver CONDOR are presented.
KeywordsNonsmooth optimization Derivative-free optimization Subdifferentials Discrete gradients
Unable to display preview. Download preview PDF.
- 3.Hiriart-Urruty, J.B., Lemarechal, C.: Convex Analysis and Minimization Algorithms, vols. 1 and 2. Springer, Heidelberg (1993) Google Scholar
- 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) Google Scholar
- 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) Google Scholar
- 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) Google Scholar
- 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) Google Scholar
- 24.GAMS: The solver manuals. GAMS Development Corporation, Washington D.C. (2004) Google Scholar
- 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) Google Scholar