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
More filters
Journal ArticleDOI
Finite-time synchronization of coupled discontinuous neural networks with mixed delays and nonidentical perturbations
TL;DR: The theoretical results of this paper are more general and rigorous than the existed results which can only finite-timely synchronize or stabilize the non-delayed systems.
Journal ArticleDOI
Error estimates for non-quadratic regularization and the relation to enhancement
Elena Resmerita,Otmar Scherzer +1 more
TL;DR: In this article, error estimates for non-quadratic regularization of nonlinear ill-posed problems in Banach spaces are derived based on a few novel features: in comparison with the classical analysis of regularization methods for inverse and illposed problems where a Lipschitz continuity for the Frechet derivative is required, we use a differentiability condition with respect to the Bregman distance.
Journal ArticleDOI
A numerical approach to optimization problems with variational inequality constraints
Jiří V. Outrata,Jochem Zowe +1 more
TL;DR: Non-differentiable optimization method is used for constrained minimization of a local Lipschitz function to solve variational inequality constraints on the computation of the Stackelberg—Cournot—Nash equilibria and to the numerical solution of a class of quasi-variational inequalities.
Journal ArticleDOI
A constraint‐stabilized time‐stepping approach for rigid multibody dynamics with joints, contact and friction
Mihai Anitescu,Gary D. Hart +1 more
TL;DR: In this article, a method for achieving geometrical constraint stabilization for a linear complementarity-based time-stepping scheme for rigid multibody dynamics with joints, contact, and friction is presented.
Journal ArticleDOI
An Integral Invariance Principle for Differential Inclusions with Applications in Adaptive Control
TL;DR: In this paper, the Byrnes-Martin integral invariance principle for ordinary differential equations is extended to differential inclusions on {Bbb R}N. The extended result is applied in demonstrating the existence of adaptive stabilizers and servomechanisms for a variety of nonlinear system classes.