The equivalence of the minimal dominant set and the myopic stable set for coalition function form games

AbstractAssessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random resultsL1;L2; : : : ;Lnof the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

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On Small Perturbations of a Periodic Homogeneous Differential Inclusion with an Asymptotically Stable Set

Automation and Remote Control ◽

10.1134/s0005117919050035 ◽

2019 ◽

Vol 80 (5) ◽

pp. 834-839 ◽

Cited By ~ 2

Author(s):

M. V. Morozov

Keyword(s):

Differential Inclusion ◽

Stable Set ◽

Asymptotically Stable ◽

Small Perturbations

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Polyhedral approximations of the semidefinite cone and their application

Computational Optimization and Applications ◽

10.1007/s10589-020-00255-2 ◽

2021 ◽

Author(s):

Yuzhu Wang ◽

Akihiro Tanaka ◽

Akiko Yoshise

Keyword(s):

Initial Approximation ◽

Semidefinite Relaxation ◽

Stable Set ◽

Cutting Plane Methods ◽

Diagonally Dominant Matrices ◽

Maximum Stable Set ◽

Simple Expansion ◽

Diagonally Dominant ◽

Polyhedral Approximations ◽

Semidefinite Cone

AbstractWe develop techniques to construct a series of sparse polyhedral approximations of the semidefinite cone. Motivated by the semidefinite (SD) bases proposed by Tanaka and Yoshise (Ann Oper Res 265:155–182, 2018), we propose a simple expansion of SD bases so as to keep the sparsity of the matrices composing it. We prove that the polyhedral approximation using our expanded SD bases contains the set of all diagonally dominant matrices and is contained in the set of all scaled diagonally dominant matrices. We also prove that the set of all scaled diagonally dominant matrices can be expressed using an infinite number of expanded SD bases. We use our approximations as the initial approximation in cutting plane methods for solving a semidefinite relaxation of the maximum stable set problem. It is found that the proposed methods with expanded SD bases are significantly more efficient than methods using other existing approximations or solving semidefinite relaxation problems directly.

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