Gradient methods in an optimal control problem for a nonlinear elliptic system

1996 ◽  
Vol 37 (5) ◽  
pp. 1016-1027
Author(s):  
S. Ya. Serovaiskii
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Elliptic System ◽  
Gradient Methods ◽  
Nonlinear Elliptic System ◽  
Nonlinear Elliptic

scholarly journals Finite Element Preconditioning on Spectral Element Discretizations for Coupled Elliptic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
JongKyum Kwon ◽  
Soorok Ryu ◽  
Philsu Kim ◽  
Sang Dong Kim
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Elliptic System ◽  
Elliptic Equations ◽  
Spectral Element ◽  
Uniform Bounds ◽  
Element System ◽  
Element Discretizations

The uniform bounds on eigenvalues ofB^h2−1A^N2are shown both analytically and numerically by theP1finite element preconditionerB^h2−1for the Legendre spectral element systemA^N2u¯=f¯which is arisen from a coupled elliptic system occurred by an optimal control problem. The finite element preconditioner is corresponding to a leading part of the coupled elliptic system.

scholarly journals Solving Optimal Control Problem of Monodomain Model Using Hybrid Conjugate Gradient Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Kin Wei Ng ◽  
Ahmad Rohanin
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Conjugate Gradient ◽  
Optimization Problem ◽  
Numerical Solutions ◽  
Gradient Methods ◽  
Parabolic Partial Differential Equation ◽  
Conjugate Gradient Methods ◽  
Monodomain Model

We present the numerical solutions for the PDE-constrained optimization problem arising in cardiac electrophysiology, that is, the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model. The monodomain model consists of a parabolic partial differential equation coupled to a system of nonlinear ordinary differential equations, which has been widely used for simulating cardiac electrical activity. Our control objective is to dampen the excitation wavefront using optimal applied extracellular current. Two hybrid conjugate gradient methods are employed for computing the optimal applied extracellular current, namely, the Hestenes-Stiefel-Dai-Yuan (HS-DY) method and the Liu-Storey-Conjugate-Descent (LS-CD) method. Our experiment results show that the excitation wavefronts are successfully dampened out when these methods are used. Our experiment results also show that the hybrid conjugate gradient methods are superior to the classical conjugate gradient methods when Armijo line search is used.

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