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
The Minimization of Semicontinuous Functions: Mollifier Subgradients
TL;DR: The properties of averaged functions are studied and a new notion of subgradient is introduced based on approximations generated by mollifiers and is exploited in the design of minimization procedures.
Book
Adaptive monotone multigrid methods for nonlinear variational problems
TL;DR: A new and promising way of constructing fast solvers for the corresponding discretized problems providing globally convergent iterative schemes with (asymptotic) multigrid convergence speed is described.
Journal ArticleDOI
A Subdifferential Condition for Calmness of Multifunctions
René Henrion,Jirí V. Outrata +1 more
TL;DR: In this paper, a condition ensuring calmness of a class of multifunctions between finite-dimensional spaces is derived in terms of subdifferential concepts developed by Mordukhovich, which allows one to derive dual constraint qualifications in nonlinear optimization that are weaker than conventional ones but still sufficient for the existence of Lagrange multipliers.
Journal ArticleDOI
Stability theory for parametric generalized equations and variational inequalities via nonsmooth analysis
TL;DR: In this paper, the authors develop a stability theory for broad classes of parametric generalized equations and variational inequalities in finite dimensions, and prove new criteria for the existence of Lipschitzian multivalued and single-valued implicit functions.
Journal ArticleDOI
Discrete variational Hamiltonian mechanics
Sanjay Lall,Matthew West +1 more
TL;DR: In this article, the Pontryagin principle is used to show the relationship between generating functions and symplectic integrators, and connections to optimal control theory and numerical algorithms are discussed.