Title: Theoretical and numerical study of the performance of 'Pincus' optimisation method

Authors: Majed Chemkhi; Mohamed Jebalia; Azmi Makhlouf

Addresses: LAMSIN Laboratory, National Engineer School of Tunis, University of Tunis El Manar, BP37, Le Belvédère 1002, Tunis, Tunisia ' Department of Mathematics and Statistics, College of Science, King Faisal University, Saudi Arabia; LAMSIN Laboratory, University of Tunis El Manar, Tunisia ' LAMSIN Laboratory, National Engineer School of Tunis, University of Tunis El Manar, BP37, Le Belvédère 1002, Tunis, Tunisia

Abstract: In this work, we are interested in the numerical and theoretical study of the so called 'Pincus algorithm', which is a stochastic optimisation method. It is based on a representation of the optimum as a limit of a ratio of two expectations, computed using a Monte Carlo approximation. First, we theoretically study the convergence of Pincus algorithm. Then, numerical computations are performed: we show the algorithm advantages and limits, in comparison with other methods in terms of robustness, speed and dependence on the dimension.

Keywords: numerical optimisation; Pincus algorithm; stochastic optimisation; law of large numbers; Monte Carlo approximation.

DOI: 10.1504/IJMMNO.2016.081886

International Journal of Mathematical Modelling and Numerical Optimisation, 2016 Vol.7 No.3/4, pp.259 - 292

Received: 17 Dec 2015
Accepted: 02 Jun 2016

Published online: 27 Jan 2017 *

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