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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
Convergence Properties of the Inexact Levenberg-Marquardt Method under Local Error Bound Conditions
TL;DR: This paper shows that the inexact Levenberg-Marquardt method (ILMM), which does not require computing exact search directions, has a superlinear rate of convergence under the same local error bound assumption and proposes the ILMM with Armijo's stepsize rule that has global convergence under mild conditions.
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Sample average approximation methods for a class of stochastic variational inequality problems
TL;DR: Under some moderate conditions, it is shown that the sample average approximated SVIP has a solution with probability one and with probability approaching one exponentially fast with the increase of sample size, the solution converges to its true counterpart.
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Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints
TL;DR: A new splitting approach is developed to these models, optimality conditions and duality theory, which is used to construct special decomposition methods for stochastic dominance constraints of second order.
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Global stabilization of rigid formations in the plane
Yu-Ping Tian,Qin Wang +1 more
TL;DR: A constructive perturbation method is proposed and combined with the conventional gradient control law that stabilizes the desired rigid formation in a global sense for all initial conditions except the case when a pair of communicating agents happen to have the same initial location.
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On the optimal design of columns against buckling
Steven J. Cox,Michael L. Overton +1 more
TL;DR: In this paper, the authors established existence, derived necessary conditions, infer regularity, and construct and test an algorithm for the maximization of a column's Euler buckling load under a variety of boundary conditions over a general class of admissible designs.