Sensitivity and stability in NLP ILL-POSED VARIATIONAL PROBLEMS

Kaplan, A.; Tichatschke, R.

doi:10.1007/0-306-48332-7_204

Cited by 9 publications

(10 citation statements)

References 24 publications

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“…Generalization of this approach to semi-coercive problems of variational form has later been obtained by Gwinner [11], [12], [13]. See also Hlavacek [19], [20], Panagiotopoulos [27], Hlavacek, Haslinger, Necas and Lovisek [21], Kaplan and Tichatschke [22] and Spann [31] for related results. However, to the authors knowledges, a common convergence theory applicable to the numerical study of a large class of semi-coercive unilateral problems allowing rigid body motions does not exist in the literature.…”

Section: Introductionmentioning

confidence: 93%

A discretization theory for a class of semi-coercive unilateral problems

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Goeleven

2000

Numerische Mathematik

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In this paper, we present a convergence analysis applicable to the approximation of a large class of semi-coercive variational inequalities. The approach we propose is based on a recession analysis of some regularized Galerkin schema. Finite-element approximations of semi-coercive unilateral problems in mechanics are discussed. In particular, a SignoriniFichera unilateral contact model and some obstacle problem with frictions are studied. The theoretical conditions proved are in good agreement with the numerical ones. Subject Classification (1991): 49J40, 49J52, 35J20 Mathematics

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Section: Introductionmentioning

confidence: 93%

A discretization theory for a class of semi-coercive unilateral problems

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Goeleven

2000

Numerische Mathematik

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“…The relation between the Lavrentiev regularization and the Lavrentiev Prox regularization is analogous to the relation between Tychonov and Prox regularization, see [8]. We define the following optimality system:…”

Section: Prox Regularizationmentioning

confidence: 99%

Optimal distributed control of the wave equation subject to state constraints

Gugat¹,

Keimer²,

Leugering³

2009

Z Angew Math Mech

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The Lavrentiev regularization method is a tool to improve the regularity of the Lagrange multipliers in pde constrained optimal control problems with state constraints. It has already been used for problems with parabolic and elliptic systems. In this paper we consider Lavrentiev regularization for problems with a hyperbolic system, namely the scalar wave equation. We show that also in this case the regularization yields multipliers in the Hilbert space L 2 . We present numerical examples, where we compare the Lavrentiev regularization, Lavrentiev Prox regularization, a fixed point iteration to improve feasibility, and a penalty method.

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“…We refer to [8] for details. For the numerical treatment of variational inequality see also [24]. It is also well known that the variational inequality (11) is equivalent to the following equation…”

Section: Numerical Aspectsmentioning

confidence: 99%

On the Maximum Principle for Impulsive Hybrid Systems

Azhmyakov

Attia

Raisch

2008

Hybrid Systems: Computation and Control

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Abstract. In this contribution, we consider a class of hybrid systems with continuous dynamics and jumps in the continuous state (impulsive hybrid systems). By using a newly elaborated version of the Pontryagintype Maximum Principle (MP) for optimal control processes governed by hybrid dynamics with autonomous location transitions, we extend the necessary optimality conditions to a class of Impulsive Hybrid Optimal Control Problems (IHOCPs). For these problems, we obtain a concise characterization of the Impulsive Hybrid MP (IHMP), namely, the corresponding boundary-value problem and some additional relations. As in the classical case, the proposed IHMP provides a basis for diverse computational algorithms for the treatment of IHOCPs.

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Sensitivity and stability in NLP ILL-POSED VARIATIONAL PROBLEMS

Cited by 9 publications

References 24 publications

A discretization theory for a class of semi-coercive unilateral problems

A discretization theory for a class of semi-coercive unilateral problems

Optimal distributed control of the wave equation subject to state constraints

On the Maximum Principle for Impulsive Hybrid Systems

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