A Characterization of Stationary Sets for the Class of Jensen Convex Functions

2002 ◽  
pp. 25-28
Author(s):  
Roman Ger ◽  
Kazimierz Nikodem
Keyword(s):  
Convex Functions

Strict convexity, strong ellipticity, and regularity in the calculus of variations

1980 ◽  
Vol 87 (3) ◽  
pp. 501-513 ◽  
Author(s):  
J. M. Ball
Keyword(s):  
Nonlinear Systems ◽  
Calculus Of Variations ◽  
Weak Solutions ◽  
Convex Functions ◽  
Strict Convexity ◽  
Mathematical Tool ◽  
Strong Ellipticity ◽  
Regularity Of Weak Solutions ◽  
Nonlinear Elastostatics

In this paper we investigate the connection between strong ellipticity and the regularity of weak solutions to the equations of nonlinear elastostatics and other nonlinear systems arising from the calculus of variations. The main mathematical tool is a new characterization of continuously differentiable strictly convex functions. We first describe this characterization, and then explain how it can be applied to the calculus of variations and to elastostatics.

scholarly journals Greedy systems of linear inequalities and lexicographically optimal solutions

2019 ◽  
Vol 53 (5) ◽  
pp. 1929-1935
Author(s):  
Satoru Fujishige
Keyword(s):  
Convex Functions ◽  
Linear Inequalities ◽  
Convex Polyhedra ◽  
Optimal Solutions ◽  
Integral Points ◽  
System Of Linear Inequalities ◽  
Discrete Convexity ◽  
The Greedy Algorithm

The present note reveals the role of the concept of greedy system of linear inequalities played in connection with lexicographically optimal solutions on convex polyhedra and discrete convexity. The lexicographically optimal solutions on convex polyhedra represented by a greedy system of linear inequalities can be obtained by a greedy procedure, a special form of which is the greedy algorithm of J. Edmonds for polymatroids. We also examine when the lexicographically optimal solutions become integral. By means of the Fourier–Motzkin elimination Murota and Tamura have recently shown the existence of integral points in a polyhedron arising as a subdifferential of an integer-valued, integrally convex function due to Favati and Tardella [Murota and Tamura, Integrality of subgradients and biconjugates of integrally convex functions. Preprint arXiv:1806.00992v1 (2018)], which can be explained by our present result. A characterization of integrally convex functions is also given.

scholarly journals What is invexity?

1986 ◽  
Vol 28 (1) ◽  
pp. 1-9 ◽  
Author(s):  
A. Ben-Israel ◽  
B. Mond
Keyword(s):  
Mathematical Programming ◽  
Convex Functions ◽  
Constraint Qualification ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Slater Constraint Qualification ◽  
The Relationship ◽  
Unconstrained Problems ◽  
Class Of Functions

AbstractRecently it was shown that many results in Mathematical Programming involving convex functions actually hold for a wider class of functions, called invex. Here a simple characterization of invexity is given for both constrained and unconstrained problems. The relationship between invexity and other generalizations of convexity is illustrated. Finally, it is shown that invexity can be substituted for convexity in the saddle point problem and in the Slater constraint qualification.

scholarly journals Strong h-Convexity and Separation Theorems

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Teodoro Lara ◽  
Nelson Merentes ◽  
Kazimierz Nikodem
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Stability Result ◽  
Jensen Inequality ◽  
Separation Theorems

Jensen inequality for strongly h-convex functions and a characterization of pairs of functions that can be separated by a strongly h-convex function are presented. As a consequence, a stability result of the Hyers-Ulam type is obtained.

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