جستجوی مقالات مرتبط با کلیدواژه « optimal » در نشریات گروه « ریاضی »

The numerical approximation methods of the differential problems solution are numerous and various. Their classifications are based on several criteria: Consistency, precision, stability, convergence, dispersion, diffusion, speed and many others. For this reason a great interest must be given to the construction and the study of the associated algorithm: indeed the algorithm must be simple, robust, less expensive and fast. In this paper, after having recalled the δ-ziti method, we reformulat it to obtain an algorithm that does not require as many calculations as many nodes knowing that they are counted by thousands. We have, therefore, managed to optimize the number of iterations by passing for example from 103 at 10 iterations.

This paper is concerned with the stochastic linear quadratic regulator (LQR) optimal control problem in which dynamical systems have control-dependent diffusion coefficients. In fact, providing the solution to this problem leads to solving a matrix Riccati differential equation as well as a vector differential equation with boundary conditions. The present work mainly  proposes not only a novel method but also an efficient fixed-point scheme based on the spline interpolation for the numerical solution to the stochastic LQR problem. Via implementing the proposed method to the corresponding differential equation of the stochastic LQR optimal control problem, not only is the numerical solution gained, but also a suboptimal control law is obtained. Furthermore, the method application is illustrated by means of an optimal control example with the financial market problems, including two investment options.