A Recursive Algorithm for Minimizing Non-Smooth Convex Function over n-Dimensional Simplex

2008 ◽  
Author(s):  
E. Y. Morozova ◽  
Alexander M. Korsunsky
Keyword(s):  
Convex Function ◽  
Recursive Algorithm ◽  
Smooth Convex ◽  
Dimensional Simplex ◽  
Smooth Convex Function

scholarly journals Maximum cut problem: new models

2020 ◽  
Vol 10 (1) ◽  
pp. 104-112
Author(s):  
Hakan Kutucu ◽  
Firdovsi Sharifov
Keyword(s):  
Convex Hull ◽  
Convex Function ◽  
Network Flow ◽  
Optimal Solution ◽  
Submodular Function ◽  
Smooth Convex ◽  
Maximum Cut ◽  
New Models ◽  
Smooth Convex Function

In the paper, we present the maximum cut problem as maximization of a non-smooth convex function over polytope which is the convex hull of bases of the polymatroid associated with a submodular function defined on the subsets of node set of a given graph. We also formulate other new models for this problem and give necessary and enough conditions on an optimal solution in terms of network flow.

scholarly journals On the rigidity theorems for Lagrangian translating solitons in pseudo-Euclidean space II

2015 ◽  
Vol 26 (09) ◽  
pp. 1550072 ◽  
Author(s):  
R. L. Huang ◽  
R. W. Xu
Keyword(s):  
Euclidean Space ◽  
Convex Function ◽  
Smooth Convex ◽  
Bernstein Type ◽  
Translating Soliton ◽  
Rigidity Theorems ◽  
Vector Formula ◽  
Smooth Convex Function ◽  
Translating Solitons

Let u be a smooth convex function in ℝn and the graph M∇u of ∇u be a space-like translating soliton in pseudo-Euclidean space [Formula: see text] with a translating vector [Formula: see text], then the function u satisfies [Formula: see text] where ai, bi and c are constants. The Bernstein type results are obtained in the course of the arguments.

scholarly journals Sets of differentials and smoothness of convex functions

1995 ◽  
Vol 52 (1) ◽  
pp. 91-96
Author(s):  
Wee-Kee Tang
Keyword(s):  
Banach Space ◽  
Variational Principle ◽  
Convex Function ◽  
Convex Functions ◽  
Smooth Convex ◽  
Smooth Functions

Approximation by smooth convex functions and questions on the Smooth Variational Principle for a given convex function f on a Banach space are studied in connection with majorising f by C1-smooth functions.

Extreme-point solutions in Markov decision processes

1983 ◽  
Vol 20 (04) ◽  
pp. 835-842
Author(s):  
David Assaf
Keyword(s):  
Convex Function ◽  
Extreme Point ◽  
Markov Decision Processes ◽  
Convex Functions ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
Markov Decision ◽  
Full Solution

The paper presents sufficient conditions for certain functions to be convex. Functions of this type often appear in Markov decision processes, where their maximum is the solution of the problem. Since a convex function takes its maximum at an extreme point, the conditions may greatly simplify a problem. In some cases a full solution may be obtained after the reduction is made. Some illustrative examples are discussed.

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