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Computational results of the optimal control of the diffusion equation with the extended conjugate gradient algorithm. (English) Zbl 0961.65064

The authors transform the optimal control problem \[ J(u,z)= \int^1_0 \int^1_0|z^2(x,t)+ u^2(x,t)|dx dt\to \min \] subject to \(z_t= z_{xx}+ u(x,t)\) into the unconstrained problem \[ J(u,z,\mu)= \int^1_0 \int^1_0|z^2(x,t)+ u^2(x,t)|dx dt+\mu\cdot \int^1_0 \int^1_0\|z_t- z_{xx}- u(x,t)\|^2 dx dt\to \min \] and apply the extended conjugate gradient algorithm for the numerical solution. A numerical test is given.

MSC:

65K10 Numerical optimization and variational techniques
49M30 Other numerical methods in calculus of variations (MSC2010)
49J20 Existence theories for optimal control problems involving partial differential equations
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