Book ChapterDOI
The directional derivative
John M. Danskin
- pp 19-32
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In this paper, a function F(x, y) of two variables x and y is considered, where x is a point of Euclidean space R n, x = (x1,..., x n ), and y a point in some compact topological space y.Abstract:
In this chapter we shall be concerned with a function F(x, y) of two variables x and y. x is supposed to be a point of Euclidean space R n , x = (x1, ..., x n ), and y a point of some compact topological space y. While all the considerations of this chapter are carried out for a general y, the applications made in this book have y a closed bounded set in Euclidean space, and the reader may therefore if he wishes read “closed bounded Euclidean” when he sees “compact topological.”read more
Citations
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Journal ArticleDOI
Concurrent aerostructural topology optimization of a wing box
TL;DR: In this paper, a multidisciplinary framework for performing shape and topology optimization of a flexible wing structure is presented, where both the aerodynamic shape and the structural topology are optimized concurrently using gradient-based optimization.
Proceedings Article
Frank-Wolfe Splitting via Augmented Lagrangian Method
TL;DR: This work develops and analyzes the Frank-Wolfe Augmented Lagrangian (FW-AL) algorithm, a method for minimizing a smooth function over convex compact sets related by a "linear consistency" constraint that only requires access to a linear minimization oracle over the individual constraints.
Journal ArticleDOI
Modelling plankton ecosystems and the Library of Lotka
Roger Allan Cropp,John Norbury +1 more
TL;DR: In this article, the authors apply ecological axioms to the construction of complex model ecologies and demonstrate that the effect of change on plankton blooms and/or extinctions depends on the properties of the model chosen for the simulation.
Dissertation
Conservation in signal processing systems
TL;DR: The main contributions in the thesis can be broadly categorized as pertaining to a mathematical formulation of a class of conservation principles, the synthesis and identification of these principles in signal processing systems, a variational interpretation ofThese principles, and the use of these Principles in designing and gaining insight into various algorithms.
Journal ArticleDOI
Systematic errors analysis for a large dynamic range aberrometer based on aberration theory.
TL;DR: A generalized theoretical analysis based on vector aberration theory is presented, and local shift errors of the SH spot pattern as a function of the lenslet position and the local wavefront tilt over the corresponding lenslet are derived.