scispace - formally typeset
Open AccessBook

Optimization and nonsmooth analysis

Reads0
Chats0
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

Content maybe subject to copyright    Report

Citations
More filters
Journal ArticleDOI

A vector forward mode of automatic differentiation for generalized derivative evaluation

TL;DR: It is shown here that piecewise differentiable functions are lexicographically smooth in the sense of Nesterov, and that lexicographic derivatives of these functions comprise a particular subset of both the B-subdifferential and the Clarke Jacobian.
Journal ArticleDOI

Nonpathological Lyapunov functions and discontinuous Carathéodory systems

TL;DR: For these equations, sufficient conditions which guarantee both Lyapunov stability and asymptotic stability in terms of nonsmooth LyAPunov functions are given and an invariance principle is also proven.
Journal ArticleDOI

Globally Convergent Variable Metric Method for Nonconvex Nondifferentiable Unconstrained Minimization

TL;DR: In this paper, a special variable metric method is given for finding the stationary points of locally Lipschitz continuous functions which are not necessarily convex or differentiable time consuming quadratic programming subproblems do not need to be solved.
Posted Content

Uncertainty in Mechanism Design

TL;DR: In this article, the authors consider mechanism design problems with Knightian uncertainty formalized using incomplete preferences, and show that full extraction is generically possible with maximal incentive compatible mechanisms, but requires sufficient disagreement across types.
Journal ArticleDOI

Brief paper: Nonsmooth optimization for multiband frequency domain control design

TL;DR: This work extends previous work on nonsmooth H"~ synthesis to develop a nonsm Smooth optimization technique to compute local solutions to multiband synthesis problems.