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Optimization and nonsmooth analysis
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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Nondifferentiable Multiplier Rules for Optimization and Bilevel Optimization Problems
TL;DR: Necessary and sufficient optimality conditions and constraint qualifications in terms of the Michel--Penot subdifferential are given, and the results are applied to bilevel optimization problems.
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On a theorem of Danskin with an application to a theorem of Von Neumann-Sion
Pierre Bernhard,Alain Rapaport +1 more
TL;DR: Several versions of Danskin's theorem, which deal with the derivative (or subdifferential) of the upper envelope J̄(u) = supv J(u, v) of a family of functions, are given as mentioned in this paper.
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Finite-Time Consensus of Opinion Dynamics and its Applications to Distributed Optimization Over Digraph
TL;DR: Some efficient criteria for finite-time consensus of a class of nonsmooth opinion dynamics over a digraph are established and the lower and upper bounds on the finite settling time are obtained based respectively on the maximal and minimal cut capacity of the digraph.
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Semidifferentiable functions and necessary optimality conditions
TL;DR: In this article, a necessary optimality condition for constrained extremum problems with a finite-dimensional image has been proposed, while those having an infinite-dimensional one will be treated in a subsequent paper.
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Semismooth Newton Coordinate Descent Algorithm for Elastic-Net Penalized Huber Loss Regression and Quantile Regression
Congrui Yi,Jian Huang +1 more
TL;DR: An algorithm, semismooth Newton coordinate descent (SNCD), for the elastic-net penalized Huber loss regression and quantile regression in high dimensional settings and an adaptive version of the “strong rule” for screening predictors to gain extra efficiency.