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
Citations
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Journal ArticleDOI
Analysis of Generalized Pattern Searches
Charles Audet,John E. Dennis +1 more
TL;DR: A simple convergence analysis is provided that supplies detail about the relation of optimality conditions to objective smoothness properties and to the defining directions for the algorithm, and it gives previous results as corollaries.
Journal ArticleDOI
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
TL;DR: The notion of slant differentiability is recalled and it is argued that the $\max$-function is slantly differentiable in Lp-spaces when appropriately combined with a two-norm concept, which leads to new local convergence results of the primal-dual active set strategy.
Book ChapterDOI
Theory of Vector Optimization
Christiane Tammer,Alfred Göpfert +1 more
TL;DR: This work derives necessary and sufficient optimality conditions, a minimal point theorem, a vector-valued variational principle of Ekeland’s type, Lagrangean multiplier rules and duality statements, and discusses a general scalarization procedure.
Book
Numerical Optimization: Theoretical and Practical Aspects
TL;DR: This book is about the theoretical foundations of optimization algorithms, and also provides practical insights on how such methods should be implemented and applied, and provides adequate examples to help the reader understand the methods better and explore possible pitfalls.
Journal ArticleDOI
Lyapunov stability theory of nonsmooth systems
D. Shevitz,Brad Paden +1 more
TL;DR: This paper develops nonsmooth Lyapunov stability theory and LaSalle's invariance principle and Computable tests based on Filipov's differential inclusion and Clarke's generalized gradient are derived in analyzing the stability of equilibria of differential equations with discontinuous right-hand side.