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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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Journal ArticleDOI
Elliptic optimal control problems with L1-control cost and applications for the placement of control devices
TL;DR: For solving the non-differentiable optimal control problem, a semismooth Newton method is proposed that can be stated and analyzed in function space and converges locally with a superlinear rate.
Journal ArticleDOI
Linear quantile mixed models
Marco Geraci,Matteo Bottai +1 more
TL;DR: Estimation strategies to reduce the computational burden and inefficiency associated with the Monte Carlo EM algorithm are discussed and a combination of Gaussian quadrature approximations and non-smooth optimization algorithms are presented.
Book ChapterDOI
A Guide to Sample Average Approximation
TL;DR: Sample average approximation (SAA) as mentioned in this paper is a well-known technique for simulation optimization problems, and it has been shown that SAA can match the asymptotic convergence rate of stochastic approximation (SA) up to a multiplicative constant.
Posted Content
Equilibrium Bias of Technology
TL;DR: In this paper, the authors distinguish between the relative bias of technology, which concerns how the marginal product of a factor changes relative to that of another following the introduction of new technology, and the absolute bias, which looks only at the effect of new technologies on a factor's marginal product, and show that the results about relative bias do not generalize when more general menus of technological possibilities are considered.
Journal ArticleDOI
Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations
TL;DR: The concept of slant differentiability is introduced and used to study superlinear convergence of smoothing methods and semismooth methods in a unified framework and shows that a function is slantly differentiable at a point if and only if it is Lipschitz continuous at that point.