On the numerical study of an obstacle optimal control problem with source term

Ghanem, Radouen; Zireg, Billel; Sissaoui, Hocine; Boubehziz, T.

doi:10.1007/s12190-013-0728-3

Cited by 3 publications

(20 citation statements)

References 10 publications

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“…In the mathematical literature, there are few works on the numerical resolution of this kind of problem (where the control and the obstacle are the same). Ghanem et al in [18] and Kunish et al in [23] are to our knowledge, the only ones who solved numerically this kind of problems, where they have considered only the unilateral obstacle optimal control.…”

Section: Radouen Ghanem and Billel Ziregmentioning

confidence: 99%

“…By using the indirect method, Ghanem et al in [18], have solved numerically the unconstrained unilateral optimal control of obstacle type given by…”

Section: Radouen Ghanem and Billel Ziregmentioning

confidence: 99%

“…but it is necessary to add additional constraints, for example we can set ϕ H 2 (Ω) ≤ ρ 1 and ψ H 2 (Ω) ≤ ρ 1 which means that both ϕ and ψ are contained in the ball B H 2 (0, ρ 1 ) of center 0 and radius ρ 1 large enough (see Bergounioux et al [8]), for example, we can suppose that U ad = U ad ∩ B H 2 (0, ρ 1 ), where U ad = {(ϕ, ψ) ∈ U × U | ϕ ≤ ψ}, and U = H 2 (Ω) × H 1 0 (Ω). According to the result given in [18] the authors point out that, in spite of the elimination of the inequality constraint given by (6), we still get a local convergence property implied by the constraint ϕ n H 2 (Ω) ≤ R, where R is a positive radius large enough and ϕ n is an iterative solution (see [18]), hence, we are again confronted with the inequality constraint (6).…”

Section: Radouen Ghanem and Billel Ziregmentioning

confidence: 99%

“…Thus, in our opinion, to study mathematically and numerically the optimal control problem given by (7), we note that it is not necessary to suppress the constraint (6), because it is going to appear again to get the local convergence of the used algorithm for the numerical solution of the problem given by (5) (see [18]).…”

Section: Radouen Ghanem and Billel Ziregmentioning

confidence: 99%

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Numerical solution of bilateral obstacle optimal control problem, where the controls and the obstacles coincide

Ghanem¹,

Zireg²

2020

NACO

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This work is deals with the numerical solution of a bilateral obstacle optimal control problem which is similar to the one given in Bergounioux et al [9] with some modifications. It can be regarded as an extension of our previous work [18], where the main feature of the present work is that the controls and the two obstacles are the same. For the numerical resolution we follow the idea of our previous work [18]. We begin by discretizing the optimality system of the underlying problem by using finite differences schemes, then we propose an iterative algorithm. Finally, numerical examples are provides to show the efficiency of the proposed algorithm and the used scheme.

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Section: Radouen Ghanem and Billel Ziregmentioning

confidence: 99%

“…By using the indirect method, Ghanem et al in [18], have solved numerically the unconstrained unilateral optimal control of obstacle type given by…”

Section: Radouen Ghanem and Billel Ziregmentioning

confidence: 99%

Section: Radouen Ghanem and Billel Ziregmentioning

confidence: 99%

Section: Radouen Ghanem and Billel Ziregmentioning

confidence: 99%

See 2 more Smart Citations

Numerical solution of bilateral obstacle optimal control problem, where the controls and the obstacles coincide

Ghanem¹,

Zireg²

2020

NACO

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“…Using (17) and (19) and by applying LGL quadrature (15), we can approximate the performance index JOEy, u in (5a) as…”

Section: Discretization Of the Performance Indexmentioning

confidence: 99%

Direct pseudo-spectral method for optimal control of obstacle problem - an optimal control problem governed by elliptic variational inequality

Oshagh

Shamsi

2017

Math. Meth. Appl. Sci.

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In this paper, a computational technique based on the pseudo‐spectral method is presented for the solution of the optimal control problem constrained with elliptic variational inequality. In fact, our aim in this paper is to present a direct approach for this class of optimal control problems. By using the pseudo‐spectral method, the infinite dimensional mathematical programming with equilibrium constraint, which can be an equivalent form of the considered problem, is converted to a finite dimensional mathematical programming with complementarity constraint. Then, the finite dimensional problem can be solved by the well‐developed methods. Finally, numerical examples are presented to show the validity and efficiency of the technique. Copyright © 2017 John Wiley & Sons, Ltd.

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