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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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Sensitivity analysis of all eigenvalues of a symmetric matrix
TL;DR: In this paper, the first order sensitivity of all the eigenvalues of a parametrized matrix is studied and an explicit expression of them in terms of the data of the matrix is given.
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Superlinearly convergent approximate Newton methods for LC 1 optimization problems
TL;DR: This paper presents approximate Newton or SQP methods for solving nonlinear programming problems whose objective and constraint functions have locally Lipschitzian derivatives, and establishes Q-superlinear convergence of these methods under the assumption that these derivatives are semismooth.
Proceedings ArticleDOI
Mixed H 2 /H ∞ control via nonsmooth optimization
TL;DR: This work uses nonsmooth mathematical programming techniques to compute locally optimal 2/H∞-controllers, which may have a predefined structure, and proves global convergence of the method.
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Social Decision Theory: Choosing within and between Groups
TL;DR: In this article, the authors introduce a theoretical framework in which to study interdependent preferences, where the outcome of others affects the preferences of the decision maker, and characterize preferences according to the relative importance assigned to social gains and losses.
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Infinitely Many Critical Points of Non-Differentiable Functions and Applications to a Neumann-Type Problem Involving the p-Laplacian
TL;DR: For a family of functionals in a Banach space, which are possibly non-smooth and depend also on a positive real parameter, the existence of a sequence of critical points is established by mainly adapting a new technique due to Ricceri (2000, J. Appl. Math. as mentioned in this paper ).