scholarly journals Extended formulations for stable set polytopes of graphs without two disjoint odd cycles

Author(s):  
Michele Conforti ◽  
Samuel Fiorini ◽  
Tony Huynh ◽  
Stefan Weltge
Author(s):  
Yuzhu Wang ◽  
Akihiro Tanaka ◽  
Akiko Yoshise

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.


1988 ◽  
Vol 42 (3) ◽  
pp. 233-244 ◽  
Author(s):  
H. Mavromichalaki ◽  
E. Marmatsouri ◽  
A. Vassilaki

2017 ◽  
Vol 31 (2) ◽  
pp. 473-477
Author(s):  
Mark E. Ewing ◽  
Daron A. Isaac

2012 ◽  
Vol 49 (6) ◽  
pp. 1339-1346 ◽  
Author(s):  
Rebecca Browning ◽  
Steven Adamson ◽  
Shahid Karim

2016 ◽  
Vol 210 ◽  
pp. 223-234
Author(s):  
Manoel Campêlo ◽  
Victor A. Campos ◽  
Ricardo C. Corrêa ◽  
Diego Delle Donne ◽  
Javier Marenco ◽  
...  

2021 ◽  
pp. 135910452098621
Author(s):  
Rosie Oldham-Cooper ◽  
Claire Semple ◽  
Laura L. Wilkinson

We suggest a reconsideration of the role of ‘attachment orientation’ in the context of eating disorders and paediatric diabetes. Attachment orientation is a psychological construct that describes a relatively stable set of expectations and behaviours an individual relies upon in managing relationships. There is considerable evidence of an association between attachment orientation and the development and maintenance of disordered eating in individuals without diabetes, though evidence is more scant in populations with diabetes. We discuss the underpinning theory and critically examine the existing literature for the relationship between attachment orientation and disordered eating in paediatric diabetes. Finally, we draw on adjacent literatures to highlight potential future directions for research should this area be revisited. Overall, we contextualise our discussion in terms of patient-centred, holistic care that addresses the mind and body (i.e., our discussion of attachment orientation assumes a psycho-biological approach).


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