Convergence Rate of the P-Algorithm for Optimization of Continuous Functions
The P-algorithm is an adaptive algorithm for approximating the global minimum of a continuous function on an interval, motivated by viewing the function as a sample path of a Gaussian process. In this paper we analyze the convergence of the P-algorithm for arbitrary continuous functions, as well as under the assumption of Wiener measure on the objective functions. In both cases the convergence rate is described in terms of a parameter of the algorithm and a functional of the objective function.
KeywordsGlobal optimization average complexity Brownian motion.
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- oender, G. and Romeijn, E. (1995), Stochastic methods. In Handbook of Global Optimization, R. Horst and P. Pardalos, (Eds.), Kluwer Academic Publishers, Dordrecht, 829–869.Google Scholar
- Calvin, J. M. (1999), “Convergence rate of the P-algorithm,” New Jersey Institute of Technology, Computer and Information Science Report No. 99–3.Google Scholar
- Calvin, J. M. (1996), “Asymptotically optimal deterministic nonadaptive algorithms for minimization of Brownian motion,” In The Mathematics of Numerical Analysis, J. Renegar, M. Shub, and S. Smale, (Eds.), American Mathematical Society, Lectures in Applied Mathematics Vol. 32, 157–163.Google Scholar
- Zilinskas, A. (1985), “Axiomatic characterization of global optimization algorithm and investigation of its search strategy, OR Let., 4, 35–39.Google Scholar