A problem in the optimal design of networks under transverse loading

Cabib, Elio; Davini, Cesare; Ru, C. Q.

doi:10.1090/qam/1052135

Cited by 10 publications

(10 citation statements)

References 25 publications

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“…5 and Remark 1 .4). In the linear case, the previous characterization was proved in [13]. See also [12] for a similar result in the case ah (x, ç) = oç fh (x, ç) with A convex in 3…”

Section: Sufficient Conditions For the G-convergence And Representatimentioning

confidence: 64%

Homogenization of almost periodic monotone operators

Braides

Piat

Defranceschi

1992

Ann. Inst. H. Poincaré C Anal. Non Linéaire

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L'accès aux archives de la revue « Annales de l'I. H. P., section C » (http://www.elsevier.com/locate/anihpc) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Homogenization of almost periodic monotone operators

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“…5 and Remark 1 .4). In the linear case, the previous characterization was proved in [13]. See also [12] for a similar result in the case ah (x, ç) = oç fh (x, ç) with A convex in 3…”

Section: Sufficient Conditions For the G-convergence And Representatimentioning

confidence: 64%

Homogenization of almost periodic monotone operators

Braides

Piat

Defranceschi

1992

Ann. Inst. H. Poincaré C Anal. Non Linéaire

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“…It may result in a mathematical formulation of the problem that allows multiple solutions (see e.g. [4]) or the uncertain misfit representation due to the irreducible measurement errors (see e.g. [5,6,7]).…”

Section: Motivationmentioning

confidence: 99%

A multi-objective memetic inverse solver reinforced by local optimization methods

Gajda-Zagórska

Schaefer

Smółka

et al. 2017

Journal of Computational Science

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Section: Motivationmentioning

confidence: 99%

“…The mathematical formulation of the problem allows multiple solutions. Sometimes, such a possibility might be formally proven (see, e.g., Cabib et al, 1990) and, more frequently, it is either anticipated from the physical evidence or reflects simply our inability to prove the uniqueness.• Uncertainty of the objective function representation. It appears because of both insufficient knowledge of the problem and the errors in data measurements and representation (see, e.g., Koper et al, 1999; Meruane and Heylen, 2009;Caicedo and Yun, 2011).…”

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confidence: 99%

A hybrid algorithm for solving inverse problems in elasticity

Barabasz

Gajda-Zagórska

Migórski

et al. 2014

International Journal of Applied Mathematics and Computer Science

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The paper offers a new approach to handling difficult parametric inverse problems in elasticity and thermo-elasticity, formulated as global optimization ones. The proposed strategy is composed of two phases. In the first, global phase, the stochastic hp-HGS algorithm recognizes the basins of attraction of various objective minima. In the second phase, the local objective minimizers are closer approached by steepest descent processes executed singly in each basin of attraction. The proposed complex strategy is especially dedicated to ill-posed problems with multimodal objective functionals. The strategy offers comparatively low computational and memory costs resulting from a double-adaptive technique in both forward and inverse problem domains. We provide a result on the Lipschitz continuity of the objective functional composed of the elastic energy and the boundary displacement misfits with respect to the unknown constitutive parameters. It allows common scaling of the accuracy of solving forward and inverse problems, which is the core of the introduced double-adaptive technique. The capability of the proposed method of finding multiple solutions is illustrated by a computational example which consists in restoring all feasible Young modulus distributions minimizing an objective functional in a 3D domain of a photo polymer template obtained during step and flash imprint lithography.Keywords: inverse problem, hierarchic genetic strategy, hybrid optimization, automatic hp-adaptive finite element method. MotivationConsiderable progress has been achieved recently in the field of inverse problems and, as a result, this area is one of the fastest growing domains in applied mathematics and computer science. It is concerned with problems that consist in finding an unknown property of a medium, or an object, from the observation of a response of this medium, or object, to a probing signal. A general framework for inverse problems provides analytical means of estimating constants in mathematical models given appropriate measurements, building mathematical models, and giving insight into the design of experiments (see, for instance, the works of Banks and Kunisch (1989), Isakov (2006), Tarantola (2005) and the references therein). Typically, inverse problems lead to mathematical models which are not well-posed in the sense of Hadamard, i.e., their solution might not be unique and/or might be unstable under data perturbations, and therefore they pose severe numerical difficulties.The growth of the area of inverse problems has largely been driven by the needs of applications both in sciences and in industry. We refer to Engl et al. (2000), Samarski and Vabishchevich (2007) or Tikhonov et al. (1995) for a description of inverse problems of different types, including inverse problems in which the equation is not specified completely as some equation coefficients are unknown, boundary inverse problems in which boundary conditions are unknown, and evolutionary inverse problems in which initial conditions are unknown.In this p...

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A problem in the optimal design of networks under transverse loading

Cited by 10 publications

References 25 publications

Homogenization of almost periodic monotone operators

Homogenization of almost periodic monotone operators

A multi-objective memetic inverse solver reinforced by local optimization methods

A hybrid algorithm for solving inverse problems in elasticity

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