A Primal-Dual Active Set Method for Bilaterally Control Constrained Optimal Control of the Navier–Stokes Equations

2005 ◽  
Vol 25 (7-8) ◽  
pp. 657-683 ◽  
Author(s):  
J. C. De los Reyes
Keyword(s):  
Optimal Control ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Active Set ◽  
Navier Stokes Equations ◽  
Active Set Method ◽  
Constrained Optimal Control ◽  
Primal Dual

scholarly journals Mesh independence and fast local convergence of a primal-dual active-set method for mixed control-state constrained elliptic control problems

2007 ◽  
Vol 49 (1) ◽  
pp. 1-38 ◽  
Author(s):  
M. Hintermüller
Keyword(s):  
Optimal Control ◽  
Numerical Test ◽  
Control Problems ◽  
Active Set ◽  
Active Set Method ◽  
Constrained Optimal Control ◽  
Mixed Control ◽  
Mesh Independence ◽  
Primal Dual ◽  
Control State

A class of mixed control-state constrained optimal control problems for elliptic partial differential equations arising, for example, in Lavrentiev-type regularized state constrained optimal control is considered. Its numerical solution is obtained via a primal-dual activeset method, which is equivalent to a class of semi-smooth Newton methods. The locally superlinear convergence of the active-set method in function space is established, and its mesh independence is proved. The paper contains a report on numerical test runs including a comparison with a short-step path-following interior-point method and a coarse-to-fine mesh sweep, that is, a nested iteration technique, for accelerating the overall solution process. Finally, convergence and regularity properties of the regularized problems with respect to a vanishing Lavrentiev parameter are considered. 2000 Mathematics subject classification: primary 65K05; secondary 90C33.

Pontryagin maximum principle and second order optimality conditions for optimal control problems governed by 2D nonlocal Cahn–Hilliard–Navier–Stokes equations

Analysis ◽  
2020 ◽  
Vol 40 (3) ◽  
pp. 127-150
Author(s):  
Tania Biswas ◽  
Sheetal Dharmatti ◽  
Manil T. Mohan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stokes Equations ◽  
Minimum Principle ◽  
Immiscible Fluids ◽  
Second Order ◽  
Navier Stokes ◽  
Distributed Optimal Control ◽  
Navier Stokes Equations

AbstractIn this paper, we formulate a distributed optimal control problem related to the evolution of two isothermal, incompressible, immiscible fluids in a two-dimensional bounded domain. The distributed optimal control problem is framed as the minimization of a suitable cost functional subject to the controlled nonlocal Cahn–Hilliard–Navier–Stokes equations. We describe the first order necessary conditions of optimality via the Pontryagin minimum principle and prove second order necessary and sufficient conditions of optimality for the problem.

scholarly journals Optimal Control of Thermally Coupled Navier Stokes Equations

1995 ◽  
pp. 199-214 ◽  
Author(s):  
Kazufumi Ito ◽  
Jeffrey S. Scroggs ◽  
Hien T. Tran
Keyword(s):  
Optimal Control ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations
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