Displaying similar documents to “Optimality conditions for constrained convex parabolic control problems via duality.”

On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Ira Neitzel, Fredi Tröltzsch (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated...

The gradient projection method for solving an optimal control problem

M. Farag (1997)

Applicationes Mathematicae

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A gradient method for solving an optimal control problem described by a parabolic equation is considered. The gradient projection method is applied to solve the problem. The convergence of the projection algorithm is investigated.

On an optimal control problem for a quasilinear parabolic equation

S. Farag, M. Farag (2000)

Applicationes Mathematicae

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An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.

A nonmonotone line search for the LBFGS method in parabolic optimal control problems

Omid Solaymani Fard, Farhad Sarani, Akbar Hashemi Borzabadi, Hadi Nosratipour (2019)

Kybernetika

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In this paper a nonmonotone limited memory BFGS (NLBFGS) method is applied for approximately solving optimal control problems (OCPs) governed by one-dimensional parabolic partial differential equations. A discretized optimal control problem is obtained by using piecewise linear finite element and well-known backward Euler methods. Afterwards, regarding the implicit function theorem, the optimal control problem is transformed into an unconstrained nonlinear optimization problem (UNOP)....

Optimality conditions for semilinear parabolic equations with controls in leading term

Hongwei Lou (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of homogenizing spike variation. Results for problems with state constraints are also stated.

Optimal Control of Semilinear Parabolic Equations with State-Constraints of Bottleneck Type

Maïtine Bergounioux, Fredi Tröltzsch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider optimal distributed and boundary control problems for semilinear parabolic equations, where pointwise constraints on the control and pointwise mixed control-state constraints of bottleneck type are given. Our main result states the existence of regular Lagrange multipliers for the state-constraints. Under natural assumptions, we are able to show the existence of bounded and measurable Lagrange multipliers. The method is based on results from the theory of continuous linear...