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
Citations
More filters
Journal ArticleDOI
Approximate mean value theorem for upper subderivatives
TL;DR: In this article, the authors give a mean value theorem for a lower semicontinuous function f on a Banach space, using the upper subderivatives defined by Rockafellar.
Ghosts and machines : regularized variational methods for interactive simulations of multibodies with dry frictional contacts
TL;DR: In this article, a time-discrete formulation of the variational principle of mechanics is used to provide a consistent theoretical framework for the construction and analysis of low-order integration methods.
Book ChapterDOI
A Survey on Direct Search Methods for Blackbox Optimization and their Applications
TL;DR: This chapter surveys algorithms for this class of problems, including a supporting convergence analysis based on the nonsmooth calculus and lists numerous published applications of these methods to real optimization problems.
Journal ArticleDOI
The system of generalized vector equilibrium problems with applications
TL;DR: A maximal element theorem is used to establish existence results for a solution of these systems of generalized vector equilibrium problems, which includes as special cases the system of generalized implicit vector variational inequality problems.
Journal ArticleDOI
Brief Backstepping for nonsmooth systems
TL;DR: The paper presents a constructive control design for integrator backstepping in nonsmooth systems based on non smooth analysis and Lyapunov stability that is applicable to a larger class of systems.