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Optimization and nonsmooth analysis
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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
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On the structure of the critical set of non-differentiable functions with a weak compactness condition
TL;DR: In this article, the nature of critical points generated by Ghoussoub's type min-max principle for locally Lipschitz continuous functionals fulfilling a weak Palais-Smale assumption, which contains the so-called non-smooth Cerami condition, is investigated.
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Disappearing Cryptography: Information Hiding: Steganography and Watermarking
TL;DR: This new edition of this best-selling book on cryptography and information hiding delineates a number of different methods to hide information in all types of digital media files, and includes 5 completely new chapters that introduce newer more sophisticated and refined cryptographic algorithms and techniques capable of withstanding the evolved forms of attack.
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Bilevel programming for the continuous transport network design problem
TL;DR: Four variants of gradient-based methods are presented and numerical comparisons are widely made with the previous on three kinds of test networks to solve CNDP generally where the Karush-Kuhn-Tucker points can be obtained.
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Implicit partial differential equations
TL;DR: In this paper, the authors compare first and second order PDE's with viscosity solutions, and give some preliminary results existence theorems for systems of partial differential equations, including singular values case.
Journal ArticleDOI
Nash-Cournot Equilibria in Electric Power Markets with Piecewise Linear Demand Functions and Joint Constraints
Benjamin F. Hobbs,Jong-Shi Pang +1 more
TL;DR: A more general model of Nash-Cournot competition on networks is proposed that accounts for nonsmooth demand functions, including concave piecewise-linear demand curves and joint constraints that include variables from other generating companies within the profit maximization problems for individual generators.