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
Proceedings ArticleDOI
Set-valued differentials and the hybrid maximum principle
TL;DR: In this paper, an axiomatic definition of generalized differentiation theory (GDT) and a precise statement of the directional open mapping property (DOMP) are given, and the definitions of the two most recent GDTs, namely, the generalized differential quotients (GDQs) and path integral generalized differentials (PIGDs), are outlined.
Journal ArticleDOI
Generalized monotonicity and generalized convexity
TL;DR: In this paper, it was shown that the generalized monotonicity of lower semicontinuous functions can be characterized via the quasimonotonicity, pseudomonotonicity and strict pseudomonoticity of different types of generalized derivatives, including the Dini, Dini-Hadamard, Clarke and Rockafellar derivatives.
Journal ArticleDOI
Mathematical Programs with Equilibrium Constraints: Enhanced Fritz John-conditions, New Constraint Qualifications, and Improved Exact Penalty Results
TL;DR: This work proves an enhanced version of the Fritz John conditions that motivates the introduction of some new CQs which can be used in order to obtain, for the first time, a completely elementary proof of the fact that a local minimum is an M-stationary point under one of these CQS.
Journal ArticleDOI
Optimal control of a non-smooth semilinear elliptic equation
TL;DR: In this article, an optimal control problem governed by a non-smooth semilinear elliptic equation is considered and the control-to-state mapping is shown to be directionally differentiable and precisely characterize its Bouligand subdifferential.