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Optimization and nonsmooth analysis

Frank H. Clarke
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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.

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Journal ArticleDOI

Lexicographic differentiation of nonsmooth functions

Yu. Nesterov
- 01 Nov 2005 - 
TL;DR: It is shown that an appropriately defined lexicographic subdifferential ensures a more rigorous selection of a candidate optimal solution than the sub differential of Clarke.
Journal ArticleDOI

Constraint qualifications and Lagrange multipliers in nondifferentiable programming problems

Abderrahim Jourani
- 01 Jun 1994 - 
TL;DR: In this paper, the nonvacuity and boundedness of the Lagrange multiplier sets for general non-differentiable programming problems are investigated, and the relationships with various constraint qualifications are investigated.
Journal ArticleDOI

Boundary hemivariational inequality of parabolic type

Stanisław Migórski, +1 more
- 01 May 2004 - 
TL;DR: In this article, the authors considered a parabolic hemivariational inequality with a nonmonotone multivalued boundary condition and with a time-dependent pseudomonotone operator.
Posted Content

A Majorized ADMM with Indefinite Proximal Terms for Linearly Constrained Convex Composite Optimization

Min Li, +2 more
- 05 Dec 2014 - 
TL;DR: In this article, a majorized alternating direction method of multipliers (ADMM) with indefinite proximal terms for solving linearly constrained $2$-block convex composite optimization problems was presented.
BookDOI

Advances in mechanics and mathematics

David Yang Gao, +1 more
TL;DR: Motreanu and Naniewicz as mentioned in this paper described the dynamics of rigid body systems with unilateral or friction-constraint constraints, and presented a model of Dendritic Growth with Convection.