A global optimization method based on multi-unit extremum-seeking for scalar nonlinear systems

Finding the global optimum of a nonlinear function is a challenging task that could involve a large number of functional evaluations. In this paper, an algorithm that uses tools from the domain of extremum-seeking is shown to provide an efficient deterministic method for global optimization. Extremum-seeking schemes typically find the local optimum by controlling the gradient to zero. In this paper, the multi-unit framework is used, where the gradient is estimated by finite difference for a given offset between the inputs. The gradient is pushed to zero by an integral controller. It is shown that if the offset is reduced to zero, the system can be made to converge to the global optimum of nonlinear continuous static. scalar maps. The result is extended to constrained problems where a switching control strategy is employed. Several illustrative examples are presented and the proposed method is compared with other methods of global optimization. (c) 2010 Elsevier Ltd. All rights reserved.