Opuscula Math. 34, no. 4 (2014), 699-724
Dynamic programming approach to structural optimization problem - numerical algorithm
Piotr Fulmański
Andrzej Nowakowski
Jan Pustelnik
Abstract.
In this paper a new shape optimization algorithm is presented. As a model application we consider state problems related to fluid mechanics, namely the Navier-Stokes equations for viscous incompressible fluids. The general approach to the problem is described. Next, transformations to classical optimal control problems are presented. Then, the dynamic programming approach is used and sufficient conditions for the shape optimization problem are given. A new numerical method to find the approximate value function is developed.
Keywords:
sufficient optimality condition, elliptic equations, optimal shape control, structural optimization, stationary Navier-Stokes equations, dynamic programming, numerical approximation.
Mathematics Subject Classification:
49K20, 49J20, 93C20, 35L20.
About the authors ▼
Piotr Fulmański
University of Łódź, Faculty of Mathematics and Computer Science Computer Science, Banacha 22, 90-238 Łódź, Poland
Andrzej Nowakowski
University of Łódź, Faculty of Mathematics and Computer Science Computer Science, Banacha 22, 90-238 Łódź, Poland
Jan Pustelnik
University of Łódź, Faculty of Mathematics and Computer Science Computer Science, Banacha 22, 90-238 Łódź, Poland
About the article ▼
Received: 2014-02-02.
Accepted: 2014-05-10.
Cite this article as ▼
Piotr Fulmański, Andrzej Nowakowski, Jan Pustelnik, Dynamic programming approach to structural optimization problem - numerical algorithm, Opuscula Math. 34, no. 4 (2014), 699-724,
http://dx.doi.org/10.7494/OpMath.2014.34.4.699.
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