Journal ArticleDOI
On solving a non-convex quadratic programming problem involving resistance distances in graphs
Dipti Dubey,S. K. Neogy +1 more
TLDR
This paper considers 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 shows 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 quadratics programming problem.Abstract:
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 $$x^{T}Rx$$ 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.read more
Citations
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Variance and covariance of distributions on graphs
TL;DR: A theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes, and shows how the maximum-variance distribution can be interpreted as a core-periphery measure.
Journal ArticleDOI
Variance and Covariance of Distributions on Graphs
TL;DR: In this article , the authors developed a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes.
Journal ArticleDOI
A universal noise-suppressing neural algorithm framework aided with nonconvex activation function for time-varying quadratic programming problems
Yingyi Sun,Jiongyi Cao,Chunxu Li +2 more
TL;DR: In this paper , a nonconvex function activated implicit ZNN (NIZNN) model and a noise-suppressing implicit zeroing neural network (NNSIZNN) were proposed by the inspiration of the conventional ZNN model from a control-based framework, which guarantees an effective solution for TVQPPs in the presence of different noises.
Book ChapterDOI
Copositive Optimization and Its Applications in Graph Theory
S. K. Neogy,Vatsalkumar N. Mer +1 more
TL;DR: In this article, the diversity of copositive optimization formulations in different domains of optimization is demonstrated, and the role of copositivity for local and global optimality conditions is discussed.
References
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Journal ArticleDOI
A polynomial-time algorithm for a class of linear complementary problems
TL;DR: An algorithm is presented that solves the problem of finding n-dimensional vectors in O(n3L) arithmetic operations by tracing the path of centers by identifying the centers of centers of the feasible region.
Journal ArticleDOI
Resistance distance and Laplacian spectrum
TL;DR: In this paper, the Laplacian eigenvalues and eigenvectors of a connected, molecular graph G are expressed in terms of the resistance matrix of the graph.
Journal ArticleDOI
Two-person nonzero-sum games and quadratic programming
Olvi L. Mangasarian,H Stone +1 more
TL;DR: In this paper, it was shown that a necessary and sufficient condition that a point be a Nash equilibrium point of a two-person, nonzero-sum game with a finite number of pure strategies is that the point is a solution of a single programming problem with linear constraints and a quadratic objective function that has a global maximum of zero.
Journal ArticleDOI
A Simple Method for Computing Resistance Distance
TL;DR: In this article, the Laplacian matrix of the graph G is used to compute the resistance distance between two vertices v i and v j of a (connected, molecular) graph G and the effective resistance between the respective two points of an electrical network, such that the resistance of any edge is unity.
Journal ArticleDOI
Regularity versus Degeneracy in Dynamics, Games, and Optimization: A Unified Approach to Different Aspects
TL;DR: In this paper, links are established between optimality conditions for quadratic optimization problems, qualitative properties in the nonlinear selection replicator dynamics, and central solution concepts of evolutionary game theory.
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