Open AccessStrict convexity of the objective function and uniqueness of the maximum point in a model with three arbitrary random priorities
Author(s) -
И. В. Павлов,
N V Neumerzhitskaia,
S I Uglich,
T A Volosatova
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2131/3/032001
Subject(s) - uniqueness , convexity , corollary , generalization , function (biology) , mathematics , point (geometry) , mathematical economics , mathematical optimization , pure mathematics , combinatorics , mathematical analysis , economics , finance , geometry , evolutionary biology , biology
The main result of this paper is the proof of the strict concavity of some function of integral form depending on three random variables, which we call priorities. This function is an objective function in the so-called model with priorities, in which the arbiter, following expert opinions, distributes funds among the enterprises and institutions under his jurisdiction. This result implies an important corollary about the existence and uniqueness of a local maximum point (which is also a global maximum point) of the objective function. This is a significant generalization of the corresponding result of N.V. Neumezhitskaia, S.I. Uglich and T.A. Volosatova, published in December 2020.