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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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Journal ArticleDOI
Necessary Conditions for Optimal Control Problems Involving Nonlinear Differential Algebraic Equations
TL;DR: In this article, the authors derived necessary conditions of optimality for optimal control problems involving a coupled set of differential and algebraic equations (DAEs) for nonconvex velocity sets.
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A Trust Region Method for Solving Generalized Complementarity Problems
TL;DR: Global convergence and, under a nonsingularity assumption, local Q-superlinear (or quadratic) convergence of the algorithm are established and calculation of a generalized Jacobian is discussed and numerical results are presented.
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Convexity in Hamilton--Jacobi Theory I: Dynamics and Duality
TL;DR: Value functions propagated from initial or terminal costs and constraints by way of a differential inclusion, or more broadly through a Lagrangian that may take on $\infty$, are studied in the case where convexity persists in the state argument and a extended "method of characteristics" is developed.
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Distributed optimization for multi-agent systems with constraints set and communication time-delay over a directed graph
TL;DR: A novel distributed algorithm is developed to solve the problem of distributed optimization for a multi-agent system with constraints set and communication time-delay over a directed graph, where auxiliary state variables are exchanged to compensate the nonzero gradient of local cost function and accelerate the convergence of estimate states to the optimal point.
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Robust linear anti‐windup synthesis for recovery of unconstrained performance
TL;DR: In this paper, an optimal LMI-based synthesis procedure is provided for static and plant-order linear anti-windup augmentation and the performance of the resulting design strategy is shown via a simulation example.