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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
Convex composite multi-objective nonsmooth programming
TL;DR: This paper examines nonsmooth constrained multi-objective optimization problems where the objective function and the constraints are compositions of convex functions, and locally Lipschitz and Gâteaux differentiable functions.
Journal ArticleDOI
Adaptive Information Collection by Robotic Sensor Networks for Spatial Estimation
R. Graham,Jorge E. Cortes +1 more
TL;DR: It is shown that the solutions to a novel generalized disk-covering problem are solutions to the optimal sampling problem of minimizing the maximum predictive variance of the estimator over the space of network trajectories.
Journal ArticleDOI
Periodic solutions of non-autonomous second order systems
TL;DR: In this article, an existence theorem of periodic solutions of non-autonomous second order systems with classical theorems of variational calculus was obtained. But the existence theorem was not proved for the case of second-order systems.
Journal ArticleDOI
The Euler and Weierstrass conditions for nonsmooth variational problems
A. D. Ioffe,R. T. Rockafellar +1 more
TL;DR: In this article, the Lagrangian function in the calculus of variations was shown to not be Lipschitz continuous or convex in the velocity argument in a nonsmooth, nonconvex setting, and a full subgradient version of Euler's equation was derived for an arc that furnishes a local minimum in the classical weak sense.
ReportDOI
Filter Pattern Search Algorithms for Mixed Variable Constrained Optimization Problems
TL;DR: This class combines and extends the Audet-Dennis Generalized Pattern Search algorithms for bound constrained mixed variable optimization, and their GPS-filter algorithms for general nonlinear constraints, and is believed to be the first algorithm with provable convergence results to directly target this class of problems.