A quadratic programming approach to the determination of an upper bound on the weighted stability number

2001 ◽  
Vol 132 (3) ◽  
pp. 569-581 ◽  
Author(s):  
Carlos J. Luz ◽  
Domingos M. Cardoso
Keyword(s):  
Quadratic Programming ◽  
Upper Bound ◽  
Programming Approach ◽  
Stability Number ◽  
Weighted Stability

scholarly journals A characterization of the weighted version of McEliece–Rodemich–Rumsey–Schrijver number based on convex quadratic programming

2015 ◽  
Vol 07 (04) ◽  
pp. 1550050
Author(s):  
Carlos J. Luz
Keyword(s):  
Quadratic Programming ◽  
Discrete Math ◽  
Convex Quadratic Programming ◽  
Stability Number ◽  
Weighted Version ◽  
Similar Characterization ◽  
Number Formula ◽  
Weighted Stability ◽  
Theta Number

For any graph [Formula: see text] Luz and Schrijver [A convex quadratic characterization of the Lovász theta number, SIAM J. Discrete Math. 19(2) (2005) 382–387] introduced a characterization of the Lovász number [Formula: see text] based on convex quadratic programming. A similar characterization is now established for the weighted version of the number [Formula: see text] independently introduced by McEliece, Rodemich, and Rumsey [The Lovász bound and some generalizations, J. Combin. Inform. Syst. Sci. 3 (1978) 134–152] and Schrijver [A Comparison of the Delsarte and Lovász bounds, IEEE Trans. Inform. Theory 25(4) (1979) 425–429]. Also, a class of graphs for which the weighted version of [Formula: see text] coincides with the weighted stability number is characterized.

scholarly journals Graphs with least eigenvalue -2 attaining a convex quadratic upper bound for the stability number

2006 ◽  
Vol 133 (31) ◽  
pp. 41-55 ◽  
Author(s):  
D.M. Cardoso ◽  
D. Cvetkovic
Keyword(s):  
Quadratic Programming ◽  
Upper Bound ◽  
Convex Quadratic Programming ◽  
Line Graphs ◽  
Regular Graphs ◽  
Stability Number ◽  
Least Eigenvalue ◽  
Regularity Properties ◽  
New Construction ◽  
The Stability

In this paper we study the conditions under which the stability number of line graphs, generalized line graphs and exceptional graphs attains a convex quadratic programming upper bound. In regular graphs this bound is reduced to the well known Hoffman bound. Some vertex subsets inducing sub graphs with regularity properties are analyzed. Based on an observation concerning the Hoffman bound a new construction of regular exceptional graphs is provided. AMS Mathematics Subject Classification (2000): 05C50.

scholarly journals Solution of Quadratic Programming with Interval Variables Using a Two-Level Programming Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Syaripuddin ◽  
Herry Suprajitno ◽  
Fatmawati
Keyword(s):  
Quadratic Programming ◽  
Programming Model ◽  
Programming Models ◽  
Programming Approach ◽  
Optimum Point ◽  
Interval Variables ◽  
Interval Coefficients ◽  
Optimum Solution

Quadratic programming with interval variables is developed from quadratic programming with interval coefficients to obtain optimum solution in interval form, both the optimum point and optimum value. In this paper, a two-level programming approach is used to solve quadratic programming with interval variables. Procedure of two-level programming is transforming the quadratic programming model with interval variables into a pair of classical quadratic programming models, namely, the best optimum and worst optimum problems. The procedure to solve the best and worst optimum problems is also constructed to obtain optimum solution in interval form.

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