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Identification of parameters in initial value problems for ordinary differential equations

Chleboun, Jan, Mikeš, Karel (2015)

Programs and Algorithms of Numerical Mathematics

Scalar parameter values as well as initial condition values are to be identified in initial value problems for ordinary differential equations (ODE). To achieve this goal, computer algebra tools are combined with numerical tools in the MATLAB environment. The best fit is obtained through the minimization of the summed squares of the difference between measured data and ODE solution. The minimization is based on a gradient algorithm where the gradient of the summed squares is calculated either numerically...

Local analysis of a cubically convergent method for variational inclusions

Steeve Burnet, Alain Pietrus (2011)

Applicationes Mathematicae

This paper deals with variational inclusions of the form 0 ∈ φ(x) + F(x) where φ is a single-valued function admitting a second order Fréchet derivative and F is a set-valued map from ℝ q to the closed subsets of ℝ q . When a solution z̅ of the previous inclusion satisfies some semistability properties, we obtain local superquadratic or cubic convergent sequences.

Magnetization switching on small ferromagnetic ellipsoidal samples

François Alouges, Karine Beauchard (2009)

ESAIM: Control, Optimisation and Calculus of Variations

The study of small magnetic particles has become a very important topic, in particular for the development of technological devices such as those used for magnetic recording. In this field, switching the magnetization inside the magnetic sample is of particular relevance. We here investigate mathematically this problem by considering the full partial differential model of Landau-Lifschitz equations triggered by a uniform (in space) external magnetic field.

Magnetization switching on small ferromagnetic ellipsoidal samples

François Alouges, Karine Beauchard (2008)

ESAIM: Control, Optimisation and Calculus of Variations

The study of small magnetic particles has become a very important topic, in particular for the development of technological devices such as those used for magnetic recording. In this field, switching the magnetization inside the magnetic sample is of particular relevance. We here investigate mathematically this problem by considering the full partial differential model of Landau-Lifschitz equations triggered by a uniform (in space) external magnetic field.

Objective function design for robust optimality of linear control under state-constraints and uncertainty

Fabio Bagagiolo, Dario Bauso (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.

Objective function design for robust optimality of linear control under state-constraints and uncertainty

Fabio Bagagiolo, Dario Bauso (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.

On a shape control problem for the stationary Navier-Stokes equations

Max D. Gunzburger, Hongchul Kim, Sandro Manservisi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

An optimal shape control problem for the stationary Navier-Stokes system is considered. An incompressible, viscous flow in a two-dimensional channel is studied to determine the shape of part of the boundary that minimizes the viscous drag. The adjoint method and the Lagrangian multiplier method are used to derive the optimality system for the shape gradient of the design functional.

On identification of critical curves

Jaroslav Haslinger, Václav Horák (1990)

Aplikace matematiky

The paper deals with the problem of finding a curve, going through the interior of the domain Ω , accross which the flux ∂ u / ∂ n , where u is the solution of a mixed elliptic boundary value problem solved in Ω , attains its maximum.

On robustness of set-valued maps and marginal value functions

Armin Hoffmann, Abebe Geletu (2005)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The ideas of robust sets, robust functions and robustness of general set-valued maps were introduced by Chew and Zheng [7,26], and further developed by Shi, Zheng, Zhuang [18,19,20], Phú, Hoffmann and Hichert [8,9,10,17] to weaken up the semi-continuity requirements of certain global optimization algorithms. The robust analysis, along with the measure theory, has well served as the basis for the integral global optimization method (IGOM) (Chew and Zheng [7]). Hence, we have attempted to extend the...

On second–order Taylor expansion of critical values

Stephan Bütikofer, Diethard Klatte, Bernd Kummer (2010)

Kybernetika

Studying a critical value function ϕ in parametric nonlinear programming, we recall conditions guaranteeing that ϕ is a C 1 , 1 function and derive second order Taylor expansion formulas including second-order terms in the form of certain generalized derivatives of D ϕ . Several specializations and applications are discussed. These results are understood as supplements to the well–developed theory of first- and second-order directional differentiability of the optimal value function in parametric optimization....

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