Random gradient-free minimization of convex functions
In this paper, we prove the complexity bounds for methods of Convex Optimization based only on computation of the function value. The search directions of our schemes are normally distributed random Gaussian vectors. It appears that such methods usually need at most n times more iterations than the standard gradient methods, where n is the dimension of the space of variables. This conclusion is true both for nonsmooth and smooth problems. For the later class, we present also an accelerated scheme with the expected rate of convergence O(n[ exp ]2 /k[ exp ]2), where k is the iteration counter. For Stochastic Optimization, we propose a zero-order scheme and justify its expected rate of convergence O(n/k[ exp ]1/2). We give also some bounds for the rate of convergence of the random gradient-free methods to stationary points of nonconvex functions, both for smooth and nonsmooth cases. Our theoretical results are supported by preliminary computational experiments.
|Date of creation:||01 Jan 2011|
|Date of revision:|
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- Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
- ROMBOUTS, Jeroen V. K. & STENTOFT, Lars, 2010.
"Option pricing with asymmetric heteroskedastic normal mixture models,"
CORE Discussion Papers
2010049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Rombouts, Jeroen V.K. & Stentoft, Lars, 2015. "Option pricing with asymmetric heteroskedastic normal mixture models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 635-650.
- Jeroen V.K. Rombouts & Lars Stentoft, 2010. "Option Pricing with Asymmetric Heteroskedastic Normal Mixture Models," CREATES Research Papers 2010-44, Department of Economics and Business Economics, Aarhus University.
- Jeroen Rombouts & Lars Peter Stentoft, 2010. "Option Pricing with Asymmetric Heteroskedastic Normal Mixture Models," CIRANO Working Papers 2010s-38, CIRANO.
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