Volume 11, Issue 6
Analysis of Finite Difference Approximations of an Optimal Control Problem in Economics

Shuhua Zhang, Sergey Lapin, Na Yan & Alexander Lapin

Adv. Appl. Math. Mech., 11 (2019), pp. 1358-1375.

Published online: 2019-09

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  • Abstract

We consider an optimal control  problem which serves as a mathematical model for several problems in economics and management. The problem is the minimization of a continuous constrained   functional  governed by a linear parabolic diffusion-advection   equation  controlled in a coefficient in advection part. The additional constraint is  non-negativity of a solution of state equation. We construct and analyze several mesh schemes approximating the formulated problem using finite difference methods in space and in time. All these approximations   keep the   positivity of the solutions to mesh state problem, either unconditionally or under some additional constraints to mesh steps. This  allows us  to remove corresponding constraint from the formulation of the discrete problem to simplify its implementation. Based on theoretical estimates and numerical results, we draw conclusions about the quality of the proposed mesh schemes.

  • Keywords

Mean field game, optimal control problem, parabolic diffusion-advection equation, finite difference methods.

  • AMS Subject Headings

65M06, 65M12, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

shuhua55@126.com (Shuhua Zhang)

doforget@sina.com (Na Yan)

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