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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
Iterative Averaging of Entropic Projections for Solving Stochastic Convex Feasibility Problems
TL;DR: The main results show that this problem can be solved by an iterative method based on averaging at each step the Bregman projections with respect to f(x)=∑i=1nxi· ln xi of the current iterate onto the given sets.
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A One-Layer Recurrent Neural Network for Pseudoconvex Optimization Problems With Equality and Inequality Constraints
TL;DR: It is proved that from any initial state, the state of the proposed neural network reaches the feasible region in finite time and stays there thereafter and is convergent to an optimal solution of the related problem.
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Robust Neuro-Adaptive Containment of Multileader Multiagent Systems With Uncertain Dynamics
TL;DR: A new kind of containment controllers consisting of a linear local information-based feedback term, a neuro-adaptive approximation term and a nonsmooth feedback term are designed to complete the goal of quasi-containment in multiagent MASs subject to unknown nonlinear dynamics and external disturbances.
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Convergence analysis of gradient descent stochastic algorithms
Alexander Shapiro,Yorai Wardi +1 more
TL;DR: This paper proves convergence of a sample-path based stochastic gradient-descent algorithm for optimizing expected-value performance measures in discrete event systems.
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Optimality conditions and a smoothing trust region newton method for nonlipschitz optimization
TL;DR: This paper derives affine-scaled second order necessary and sufficient conditions for local minimizers of minimization problems with nonconvex, nonsmooth, perhaps non-Lipschitz penalty functions and proposes a global convergent smoothing trust region Newton method.