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Optimization and nonsmooth analysis
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TLDR
The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.Abstract:
1. Introduction and Preview 2. Generalized Gradients 3. Differential Inclusions 4. The Calculus of Variations 5. Optimal Control 6. Mathematical Programming 7. Topics in Analysis.read more
Citations
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Journal ArticleDOI
Inexact Newton methods for solving nonsmooth equations
José Mario Martínez,Liqun Qi +1 more
TL;DR: In this article, inexact Newton methods for solving systems of nonsmooth equations are investigated and a globally convergent inexact iteration function based method for locally Lipschitz functions is introduced.
Book ChapterDOI
On the Theory of Trajectory Tubes — A Mathematical Formalism for Uncertain Dynamics, Viability and Control
A. B. Kurzhanski,T. F. Filippova +1 more
TL;DR: A survey on trajectory tubes for differential inclusions can be found in this article, which appears to be a relevant tool for modeling uncertain dynamics and is motivated by results in nonlinear analysis, particularly, in viability theory, as well as by recent achievements in the theory of estimation and control for systems with unknown but bounded uncertainties.
Journal ArticleDOI
Band Structure Optimization of Two-Dimensional Photonic Crystals in H-Polarization
Steven J. Cox,David C. Dobson +1 more
TL;DR: In this article, an optimization-based evolution algorithm was proposed to find a material distribution within the fundamental cell which produces a maximal band gap at a given point in the spectrum for H-polarization in two dimensions.
Book ChapterDOI
Nonsmooth critical point theory and quasilinear elliptic equations
TL;DR: In this article, a generalized critical point theory for nonsmooth functionals and the existence of multiple solutions for quasilinear elliptic equations are studied. But the authors focus on the case in which f is invariant under the action of a compact Lie group.
Journal ArticleDOI
Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization
TL;DR: An extension of the velocity of the underlying Hamilton-Jacobi equation is proposed, endowed with a Hilbertian structure based on the H1 Sobolev space, for structural optimization by the level-set method.