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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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Convergence and Rate Analysis of Neural Networks for Sparse Approximation
TL;DR: An analysis of the Locally Competitive Algorithm (LCA), which is a Hopfield-style neural network that efficiently solves sparse approximation problems, shows that the LCA has desirable convergence properties, such as stability and global convergence to the optimum of the objective function when it is unique.
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Hoffman's Error Bound, Local Controllability, and Sensitivity Analysis
TL;DR: The aim is to present sufficient conditions ensuring Hoffman's error bound for lower semicontinuous nonconvex inequality systems and to analyze its impact on the local controllability, implicit function theorem for (non-Lipschitz) multivalued mappings, generalized equations, and sensitivity analysis.
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Sub-quadratic convergence of a smoothing Newton algorithm for the P 0 – and monotone LCP
TL;DR: It is proved in this paper that the proposed smoothing Newton algorithm, which is a modified version of the Qi-Sun-Zhou algorithm, has the following convergence properties: it is well-defined and any accumulation point of the iteration sequence is a solution of the P0–LCP.
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The differentiability of real functions on normed linear space using generalized subgradients
TL;DR: In this paper, the modified generalized subdifferential has been used to derive the Gâteaux differentiability of a distance function on a Banach space with rotund dual.
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Portfolio optimization with jumps and unobservable intensity process
Nicole Bäuerle,Ulrich Rieder +1 more
TL;DR: In this paper, the authors consider a financial market with one bond and one stock and assume that there is an investor who is only able to observe the stock price process and not the driving Markov chain.