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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
Citations
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Proceedings ArticleDOI
Robust connectivity of networked vehicles
Demetri Spanos,Richard M. Murray +1 more
TL;DR: A localized notion of connectedness is introduced, and a function that measures the robustness of this local connectedness to variations in position is constructed, which provides a sufficient condition for global connectedness of the network.
Journal ArticleDOI
Complementarity Functions and Numerical Experiments on Some Smoothing Newton Methods for Second-Order-Cone Complementarity Problems
X. D. Chen,Defeng Sun,Jie Sun +2 more
TL;DR: It is shown that the squared smoothing function is strongly semismooth and a new proof is provided, based on a penalized natural complementarity function, for the solution set of the second-order-cone complementarity problem being bounded.
Journal ArticleDOI
On NCP-Functions
Defeng Sun,Liqun Qi +1 more
TL;DR: This paper reformulate several NCP-functions for the nonlinear complementarity problem (NCP) from their merit function forms and study some important properties of these NCP -functions.
Journal ArticleDOI
Dynamic optimization of constrained chemical engineering problems using dynamic programming
S. A. Dadebo,Kim B. McAuley +1 more
TL;DR: In this article, the authors proposed the use of absolute error penalty functions (AEPF) in handling constrained optimal control problems in chemical engineering by posing the problem as a nonsmooth dynamic optimization problem.
Book ChapterDOI
From Convex Optimization to Nonconvex Optimization. Necessary and Sufficient Conditions for Global Optimality
TL;DR: In this paper, the main incentive comes from modelling in Applied Mathematics and Operations Research, where one may be faced with optimization problems like: minimizing (globally) a difference of convex functions, maximizing a convex function over convex sets, minimizing an indefinite quadratic form over a polyhedral convex set, etc.