Inward pointing trajectories, normality of the maximum principle and the non occurrence of the Lavrentieff phenomenon in optimal control under state constraints [PDF]
, 2013 Summary: It is well known that every strong local minimizer of the Bolza problem under state constraints satisfies a constrained maximum principle. In the absence of constraints qualifications the maximum principle may be abnormal, that is, not involving the cost functions.
Frankowska, Hélène, Tonon, Daniela
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Le Matematiche, 1999 In this paper we analyze, in the context of a Lavrentieff phenomenon, the process of homogenization for Dirichlet problems.
C. D'Apice, T. Durante, A. Gaudiello
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Optimal Control Problem for Non-linear Degenerate Parabolic Variation Inequality: Solvability and Attainability Issues [PDF]
, 2023 We investigate the optimal control problem with respect to coefficients of the degenerate parabolic variational inequality. Since problems of this type can have the Lavrentieff effect, we consider the optimal control problem in a class of so-called ...
Kasimova, Nina V. +2 more
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Il problema classico del calcolo delle variazioni: l'equazione di Du Bois-Reymond, la regolarità dei minimi e delle successioni minimizzanti [PDF]
, 2023 We consider the basic problem of the Calculus of variations of minimizing an integral functional among the absolutely continuous functions that satisfy prescribed boundary conditions. We resume the state of the art and our recent contributions concerning
Bettiol, Piernicola, Mariconda, Carlo
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Some Regularity Properties on Bolza problems in the Calculus of Variations [PDF]
, 2022 The paper summarizes the main core of the last results that we obtained in [8, 4, 17] on the regularity of the value function for a Bolza problem of a one-dimensional, vectorial problem of the calculus of variations. We are concerned with a nonautonomous
Bernis, Julien +2 more
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On the existence of weak optimal BV-controls in coefficients for linear elliptic problems
Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ, 2009 In this paper we study the optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. We adopt a weight coefficient in the main part of elliptic operator as control in BV(Ω).
I. G. Balanenko, P. I. Kogut
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H-Optimal Control in Coefficients for Dirichlet Parabolic Problems
Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ, 2010 In the paper the Dirichlet optimal control problem associated with a linear parabolic equation the coefficients of which we take as controls in L1(Ω) has been studied. Since equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness
I. G. Balanenko, P. I. Kogut
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Convergent adaptive hybrid higher-order schemes for convex minimization [PDF]
, 2021 This paper proposes two convergent adaptive mesh-refining algorithms for the hybrid high-order method in convex minimization problems with two-sided p-growth.
Carstensen, Carsten, Tran, Ngoc Tien
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No Infimum Gap and Normality in Optimal Impulsive Control Under State Constraints [PDF]
, 2020 In this paper we consider an impulsive extension of an optimal control problem with unbounded controls, subject to endpoint and state constraints. We show that the existence of an extended-sense minimizer that is a normal extremal for a constrained ...
Fusco, Giovanni, Motta, Monica
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, 2021 This article deals with the Lipschitz regularity of the ''approximate`` minimizers for the Bolza type control functional of the form \[J_t(y,u):=\int_t^T\Lambda(s,y(s), u(s))\,ds+g(y(T))\] among the pairs $(y,u)$ satisfying a prescribed initial condition
Mariconda, Carlo
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