On solving a non-convex quadratic programming problem involving resistance distances in graphs

Quadratic programming problems involving distance matrix ( D ) that arises in trees are considered in the literature by Dankelmann (Discrete Math 312:12–20, 2012 ), Bapat and Neogy (Ann Oper Res 243:365–373, 2016 ). In this paper, we consider the question of solving the quadratic programming problem...

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Published inAnnals of operations research Vol. 287; no. 2; pp. 643 - 651
Main Authors Dubey, Dipti, Neogy, S. K.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.04.2020
Springer
Springer Nature B.V
Subjects
Analysis
Business and Management
Combinatorics
Distance matrices
Graphic methods
Graphs
Mathematical programming
Matrices (mathematics)
Methods
Operations research
Operations Research/Decision Theory
Problem solving
Quadratic programming
S.I.: Game theory and optimization
Studies
Theory of Computation
India
Non-convex quadratic programming
Laplacian matrix
Polynomial time algorithm
Symmetric bimatrix game
Resistance distance
90C33
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ISSN0254-5330
1572-9338
DOI10.1007/s10479-018-3018-5

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Summary:Quadratic programming problems involving distance matrix ( D ) that arises in trees are considered in the literature by Dankelmann (Discrete Math 312:12–20, 2012 ), Bapat and Neogy (Ann Oper Res 243:365–373, 2016 ). In this paper, we consider the question of solving the quadratic programming problem of finding maximum of x T R x subject to x being a nonnegative vector with sum 1 and show that for the class of simple graphs with resistance distance matrix ( R ) which are not necessarily a tree, this problem can be reformulated as a strictly convex quadratic programming problem. An application to symmetric bimatrix game is also presented.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-018-3018-5