Open AccessBook
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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Proceedings Article
An Inverse Power Method for Nonlinear Eigenproblems with Applications in 1-Spectral Clustering and Sparse PCA
Matthias Hein,Thomas Bühler +1 more
TL;DR: In this paper, the inverse power method is generalized to nonlinear eigenproblems and applied to 1-spectral clustering and sparse PCA with non-quadratic objective and constraints.
Dissertation
Sensor based motion planning: the hierarchical generalized Voronoi graph
TL;DR: Simulations and experiments validate the development and incremental construction of the hierarchical generalized Voronoi graph (HGVG), which is a concise representation of a robot's environment that lends itself to sensor based construction in a rigorous and provably correct manner.
Journal ArticleDOI
Conewise linear elastic materials
TL;DR: In this article, a necessary and sufficient condition for a stress-strain law to be becontinous across the interface of the tension and compression subdomains is established, and the strain energy function to be strictlyconvex is derived.
Journal ArticleDOI
Mobility of bodies in contact. I. A new 2/sup nd/ order mobility index for multiple-finger grasps
Elon Rimon,Joel W. Burdick +1 more
TL;DR: It is shown that 2nd-order effects can be used to lower the effective mobility of a grasped object, and implications of this result for achieving new lower bounds on the number of contacting finger bodies needed to immobilize an object are discussed.
Journal ArticleDOI
On the identification of active constraints
James V. Burke,Jorge J. Moré +1 more
TL;DR: In this paper, a characterization of algorithms that identify the optimal active constraints in a finite number of iterations is given, with a non-degeneracy assumption which is equivalent, in the standard nonlinear programming problem, to the assumption that there is a set of strictly complementary Lagrange multipliers.