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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
Nonsmooth Finite-Time Synchronization of Switched Coupled Neural Networks
TL;DR: The obtained results in this paper include and extend the earlier works on the synchronization issue of coupled networks with Lipschitz continuous conditions and an upper bound of the settling time for synchronization is estimated.
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Efficient Computation for Sparse Load Shifting in Demand Side Management
TL;DR: A bidirectional framework for solving the demand-side management problem in a distributed way to substantially improve the search efficiency and dual fast gradient and convex relaxation are applied to tackle the sub-problem for customers' best response.
Journal ArticleDOI
A Combined Smoothing and Regularization Method for Monotone Second-Order Cone Complementarity Problems
TL;DR: This paper proposes a globally and quadratically convergent algorithm, which is based on smoothing and regularization methods, for solving monotone SOCCP, and studies strong semismoothness and Jacobian consistency, which play an important role in establishing quadratic convergence of the algorithm.
Journal ArticleDOI
A One-Layer Projection Neural Network for Nonsmooth Optimization Subject to Linear Equalities and Bound Constraints
Qingshan Liu,Jun Wang +1 more
TL;DR: It is proved that the output variables of the proposed neural network are globally convergent to the optimal solutions provided that the objective function is at least pseudoconvex.
Book
Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations With Inequality Constraints
TL;DR: In this paper, the authors present degree theoretic results for Variational-hemivariational inequalities with an asymmetric subdifferential Bibliography, including an overview of the literature.