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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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Journal ArticleDOI
Smoothing Neural Network for Constrained Non-Lipschitz Optimization With Applications
Wei Bian,Xiaojun Chen +1 more
TL;DR: Under the level bounded condition on the objective function in the feasible set, it is proved the global existence and uniform boundedness of the solutions of the SNN with any initial point in the practicable set.
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On Semismooth Newton's Methods for Total Variation Minimization
TL;DR: Based on the theory on semismooth operators,Semismooth Newton’s methods for total variation minimization are studied to show the effectiveness of the proposed algorithms.
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Finite-time cluster synchronization for a class of fuzzy cellular neural networks via non-chattering quantized controllers
TL;DR: The new analytical techniques skillfully overcome the difficulties caused by time-varying delays and cope with the uncertainties of both Filippov solution and Markov jumping, which enable the settling time explicitly to be determined.
Journal ArticleDOI
Inertial accelerated algorithms for solving a split feasibility problem
Yazheng Dang,Jie Sun,Honglei Xu +2 more
TL;DR: This paper proposes two inertial accelerated algorithms to solve the split feasibility problem, one of which is an inertial relaxed-CQ algorithm constructed by applying inertial technique to a relaxed- CQ algorithm, the other is a modified inertial relax-Cq algorithm which combines the KM method with the inertial relaxation-CZ algorithm.
Velocity extension for the level-set method and multiple eigenvalues in shape optimization ∗
TL;DR: In this paper, an extension of the velocity of the underlying Hamilton-Jacobi equation is proposed for structural optimization by the level-set method, which is endowed with a Hilbertian structure based on the H 1 Sobolev space.