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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
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Portfolio Investment with the Exact Tax Basis via Nonlinear Programming
Victor DeMiguel,Raman Uppal +1 more
TL;DR: This work characterize the optimal portfolio policy in the presence of capital gains tax when using the exact tax basis via nonlinear programming and shows that the certainty equivalent loss from using the average tax basis instead of the exact basis is very small.
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A Corollary for Nonsmooth Systems
TL;DR: In this article, two generalized corollaries to the LaSalle-Yoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right-hand sides.
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An Efficient Two-Phase ${\rm L}^{1}$ -TV Method for Restoring Blurred Images with Impulse Noise
TL;DR: A two-phase image restoration method based upon total variation regularization combined with an L1-data-fitting term for impulse noise removal and deblurring that is significantly advance over several state-of-the-art techniques with respect to restoration capability and computational efficiency is proposed.
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Fast Bundle Algorithm for Multiple-Instance Learning
TL;DR: Inspired by the latest linear-time subgradient-based methods for support vector machines, this method is linearly scalable, while not sacrificing generalization accuracy, permitting modeling on new and larger data sets in computational chemistry and other applications.
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Evolution equations governed by the sweeping process
TL;DR: In this article, a perturbed version of the classical convex sweeping process was studied and the Lipschitz constants of the solutions of the perturbations were examined. But the authors focused on the second-order sweeping process.