Optimal control of systems governed by variational inequalities

Yvon, J. P.

doi:10.1007/3-540-06583-0_26

Cited by 9 publications

(7 citation statements)

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“…At the mathematical and numerical point of view it is possible to get more details from: Kernevez (1972) for a general survey of the mathematical problems, Kernevez et al (1973) for a stochastic feedback control, Brauner and Penel (1972) for systems without michaelian assumption, Dubus (1972) for a multienzyme system and Yvon (1973) for optimal control of systems governed by variational inequalities.…”

Section: Resultsmentioning

confidence: 99%

“…A variant has been studied in J. P. Yvon (1973aYvon ( , 1973b, where the boundary films are selective only for a concentration of product smaller than h: In (5.58) we do the scalar product with 80…”

Section: J(v) = Fr O (Yl(1t)-za))2dtmentioning

confidence: 98%

“…The reaction rate is: In a variant, studied in J. P. Yvon (1973aYvon ( , 1973b, the boundary films are Enzyme E1 (resp. E2) has a range of activity at low pH (resp.…”

Section: S(ot) = S(1t) = A;mentioning

confidence: 99%

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Numerical analysis and control of some biochemical systems

Kernevez

Thomas

1975

Appl Math Optim

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Communicated by J. L. Lions RESUME Les syst~mes ~t enzymes immobilis6es sont des syst~mes off des enzymes (catalyseurs de r6actions biochimiques) sont distribu6s ~t l'int6rieur d'une membrane artificielle. Ils sont gouvern6s par le couplage entre diffusion et r6action et l'6quation typique d6crivant un tel syst~me est Os/~t-~2s/~x2 + as/(1 + s) = 0, s = s(x,t) 6tant la concentration du substrat.Dans une premiere partie sont d6crits plusieurs syst~mes enzymatiques, ainsi que leurs 6quations (aux d6riv6es partielles).Une seconde partie est consacr6e aux m6thodes math6matiques utilis6es pour d6montrer l'existence et l'unicit6 d'une solution pour ces 6quations.Dans la troisi~me partie sont donn6es les m6thodes num&iques utilis6es pour obtenir une solution approch6e.La derni~re partie traite de probl~mes de contrfle en boucle ouverte dans ces syst~mes biochimiques.L'existence d'un contr61e optimal est d6montr6e, le gradient de la fonetion coot est trouv6 en utilisant l'6tat adjoint et l'algorithme de "steepest descent" est utilis6. ABSTRACTImmobilized enzyme systems are systems where enzyme(s) (catalyst(s) of biochemical reaction(s)) is (are) distributed inside an artificial membrane. They are governed by the coupling between diffusion and reaction, and the typical equation describing such a system is 8s/Ot-~2s/Sx2 + ~rs/(1 + s) = O, s = s(x,t) denoting the substrate concentration.In a first part are described several enzyme systems, together with their (partial differential) equations.A second part is devoted to the mathematical methods used to prove existence and uniqueness of a solution for these equations.

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Section: Resultsmentioning

confidence: 99%

Section: J(v) = Fr O (Yl(1t)-za))2dtmentioning

confidence: 98%

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Numerical analysis and control of some biochemical systems

Kernevez

Thomas

1975

Appl Math Optim

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“…Nevertheless, the results mentioned in the works above, with the exception of those of Yvon in [43,44], stop short of developing numerical methods and were mainly concerned with the derivation of first-order optimality conditions. In [44], the solution operator S was smoothed and a sequence of related optimal control problems was solved, thus foreshadowing some of the more popular methods currently in use, cf.…”

Section: Introductionmentioning

confidence: 96%

“…In [44], the solution operator S was smoothed and a sequence of related optimal control problems was solved, thus foreshadowing some of the more popular methods currently in use, cf. [17,18,39].…”

Section: Introductionmentioning

confidence: 99%

Elliptic Mathematical Programs with Equilibrium Constraints in Function Space: Optimality Conditions and Numerical Realization

Hintermüller

Laurain

Löbhard

et al. 2014

International Series of Numerical Mathematics

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Recent advances in the analytical as well as numerical treatment of classes of elliptic mathematical programs with equilibrium constraints (MPECs) in function space are discussed. In particular, stationarity conditions for control problems with point tracking objectives and subject to the obstacle problem as well as for optimization problems with variational inequality constraints and pointwise constraints on the gradient of the state are derived. For the former problem class including the case of L 2 -tracking-type objectives (rather than pointwise ones) a bundle-free solution method as well as adaptive finite element discretizations are introduced. Moreover, the analytical and numerical treatment of shape design problems subject to elliptic variational inequality constraints is highlighted. With respect

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On Optimal Control and Identification of Processes Governed by Parabolic Differential Equations of Second Order

Wolfersdorf

1977

Z Angew Math Mech

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Optimal control of systems governed by variational inequalities

Cited by 9 publications

References 1 publication

Numerical analysis and control of some biochemical systems

Numerical analysis and control of some biochemical systems

Elliptic Mathematical Programs with Equilibrium Constraints in Function Space: Optimality Conditions and Numerical Realization

On Optimal Control and Identification of Processes Governed by Parabolic Differential Equations of Second Order

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