Continuous Generalized Gradients for Nonsmooth Functions

1988 ◽  
pp. 24-27 ◽  
Author(s):  
V. F. Demyanov
Keyword(s):  
Generalized Gradients ◽  
Nonsmooth Functions

Characterization of nonsmooth functions through their generalized gradients

Optimization ◽  
1991 ◽  
Vol 22 (3) ◽  
pp. 401-416 ◽  
Author(s):  
R. Ellaia ◽  
A. Hassouni
Keyword(s):  
Generalized Gradients ◽  
Nonsmooth Functions

scholarly journals Algebraic Univalence Theorems for Nonsmooth Functions

2000 ◽  
Vol 252 (2) ◽  
pp. 917-935 ◽  
Author(s):  
M.Seetharama Gowda ◽  
G Ravindran
Keyword(s):  
Nonsmooth Functions

scholarly journals Market equilibria and money

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sjur Didrik Flåm
Keyword(s):  
Fixed Point ◽  
Steady State ◽  
Value Added ◽  
Pareto Optimal ◽  
Generalized Gradients ◽  
Market Mechanisms ◽  
Mathematical Arguments ◽  
Second Welfare Theorem ◽  
Market Equilibria ◽  
Welfare Theorem

AbstractBy the first welfare theorem, competitive market equilibria belong to the core and hence are Pareto optimal. Letting money be a commodity, this paper turns these two inclusions around. More precisely, by generalizing the second welfare theorem we show that the said solutions may coincide as a common fixed point for one and the same system.Mathematical arguments invoke conjugation, convolution, and generalized gradients. Convexity is merely needed via subdifferentiablity of aggregate “cost”, and at one point only.Economic arguments hinge on idealized market mechanisms. Construed as algorithms, each stops, and a steady state prevails if and only if price-taking markets clear and value added is nil.

scholarly journals The Boosted Difference of Convex Functions Algorithm for Nonsmooth Functions

2020 ◽  
Vol 30 (1) ◽  
pp. 980-1006 ◽  
Author(s):  
Francisco J. Aragón Artacho ◽  
Phan T. Vuong
Keyword(s):  
Convex Functions ◽  
Nonsmooth Functions ◽  
Difference Of Convex Functions ◽  
Difference Of Convex

On Lipschitz behaviour of some generalized derivatives

2013 ◽  
Vol 63 (3) ◽  
Author(s):  
Dušan Bednařík ◽  
Karel Pastor
Keyword(s):  
Reference Point ◽  
Clarke Subdifferential ◽  
Generalized Derivatives ◽  
Lipschitz Property ◽  
Dini Derivative ◽  
Stable Property ◽  
Nonsmooth Functions ◽  
Clarke Derivative

AbstractThe aim of the present paper is to compare various forms of stable properties of nonsmooth functions at some points. By stable property we mean the Lipschitz property of some generalized derivatives related only to the reference point. Namely we compare Lipschitz behaviour of lower Clarke derivative, lower Dini derivative and calmness of Clarke subdifferential. In this way, we continue our study of λ-stable functions.

On Characterizations ofP- andP0-Properties in Nonsmooth Functions

2000 ◽  
Vol 25 (3) ◽  
pp. 400-408 ◽  
Author(s):  
Yoon Song ◽  
M. Seetharama Gowda ◽  
G. Ravindran
Keyword(s):  
Nonsmooth Functions
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