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Tangency, flow invariance for differential equations, and optimization problems by D. Motreanu

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Published by M. Dekker in New York .
Written in English

Subjects:

  • Differential equations, Nonlinear.,
  • Flows (Differentiable dynamical systems),
  • Mathematical optimization.

Book details:

Edition Notes

Includes bibliographical references (p. 461-476) and index.

StatementDumitru Motreanu, Nicolae Pavel.
SeriesMonographs and textbooks in pure and applied mathematics ;, 219
ContributionsPavel, N. H.
Classifications
LC ClassificationsQA372 .M74 1999
The Physical Object
Paginationx, 479 p. ;
Number of Pages479
ID Numbers
Open LibraryOL36329M
ISBN 100824773411
LC Control Number99022025

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Tangency, Flow Invariance for Differential Equations, and Optimization Problems 1st Edition. Nicolae H. Pavel, Dumitru Motreanu. This is a survey paper on optimization problems via the technique of first and second order tangent cones to a nonempty subset of a Banach space X. Such a technique is also used in the study of the flow invariance of a closed set with respect to a second order differential equation (motion on a given orbit in a force field).Cited by: 1. In this chapter, multi-criterion and topology optimization methods are discussed using Lie symmetries for differential equations. Linear combination of the infinitesimal generators associated with a given system of equations leads to some group invariant solution for the same system of equations. This chapter is devoted to a rather complete exposition of classical differential calculus. However, we present some non-classical variants which are often easier to handle. Tangency, Flow Invariance for Differential Equations, and Optimization Problems, Dekker, zbMATH Google Scholar. J.-P. Penot, Calculus Without Derivatives Author: Jean-Paul Penot.

Optimization of Differential-Algebraic Equation Systems L. T. Biegler eleven differential equations. DAE Optimization Problem Sequential Approach Discretize Vassiliadis() controls Variational Approach Pontryagin() Inefficient for constrained problems Apply a File Size: 4MB. Optimization with differential equations The discrete problem The Discrete Problem The discrete problem can be obtained using finite differences or finite elements (FEM). minY,U 1 2 PN i=1{(yi −yd,i) 2 +γu2 i} subject to AhY = BhU and Ua ≤ U ≤ Ub, Discrete objective functional Discretized differential equation Discrete inequality File Size: KB. Such optimization problems have several common characteristics and challenges, discussed in Potential Problems and Solutions. For a problem-based example of optimizing an ODE, see Fit ODE, Problem-Based. For a solver-based example, see Fit an Ordinary Differential . In section 5, augmented Lagrangians, an idea from optimization theory, enhances the convergence properties of the BDMM. In section 6, we apply the differential algorithm to two neural problems, and discuss the insen­ sitivity of BDMM to choice of parameters.

On-line books store on Z-Library | B–OK. Download books for free. Find books. flow invariance for differential equations, and optimization problems. M. Dekker. Nicolae H. Pavel, Dumitru Motreanu. Year: Language: english File: DJVU, MB 3. Tangency, Flow Invariance for Differential Equations, and Optimization Problems. \"Containing over helpful equations, Tangency, Flow Invariance for Differential Equations, and Optimization Problems is an exceptionally thorough reference for pure and applied mathematicians, nonlinear analysts, physicists, astronomers, and mechanical engineers and an excellent text for upper-level undergraduate and graduate students in. The aim of this paper is threefold: 1. (1) to introduce the notion of “quasi-tangent vector” to a subset S of a Banach manifold M and to extend the definitions (and some properties) of a generalized gradients (and tangent cones) from a Banach space E to M;. 2. (2) to apply some of the above notions to the problem of flow-invariance of a closed subset of the manifold M Cited by: Tangency, Flow Invariance for Differential Equations, and Optimization Problems (Chapman & Hall/CRC Pure and Applied Mathematics) by Nicolae H. Pavel, Dumitru Motreanu, Dumitru Montreanu Hardcover, Pages, Published by Crc Press ISBN , ISBN: