TY  - JOUR
ID  - Fulmański2014
LB  - Fulmański2014
AU  - Fulmański, Piotr
AU  - Nowakowski, Andrzej
AU  - Pustelnik, Jan
TI  - Dynamic programming approach to structural optimization problem - numerical algorithm
ST  - Dynamic programming approach to structural optimization problem - numerical algorithm
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2014
VL  - 34
IS  - 4
SP  - 699
EP  - 724
DO  - http://dx.doi.org/10.7494/OpMath.2014.34.4.699
UR  - http://dx.doi.org/10.7494/OpMath.2014.34.4.699
AB  - 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.
KW  - sufficient optimality condition
KW  - elliptic equations
KW  - optimal shape control
KW  - structural optimization
KW  - stationary Navier-Stokes equations
KW  - dynamic programming
KW  - numerical approximation
SN  - 1232-9274
ER  -