Using an interval branch-and-bound algorithm in the Hartree-Fock method

2005 ◽  
Vol 103 (5) ◽  
pp. 500-504 ◽  
Author(s):  
Carlile C. Lavor ◽  
Thiago Messias Cardozo ◽  
Marco Antonio Chaer Nascimento
Keyword(s):  
Branch And Bound ◽  
Branch And Bound Algorithm ◽  
Hartree Fock ◽  
Interval Branch And Bound

scholarly journals A generic interval branch and bound algorithm for parameter estimation

2018 ◽  
Vol 73 (3) ◽  
pp. 515-535
Author(s):  
Bertrand Neveu ◽  
Martin de la Gorce ◽  
Pascal Monasse ◽  
Gilles Trombettoni
Keyword(s):  
Parameter Estimation ◽  
Branch And Bound ◽  
Branch And Bound Algorithm ◽  
Interval Branch And Bound

Unit Commitment Solution by Branch and Bound Algorithm

2020 ◽  
Author(s):  
Bishaljit Paul ◽  
Sushovan Goswami ◽  
Dipu Mistry ◽  
Chandan Kumar Chanda
Keyword(s):  
Branch And Bound ◽  
Unit Commitment ◽  
Branch And Bound Algorithm

scholarly journals Identification of mechanical properties of arteries with certification of global optimality

2021 ◽  
Author(s):  
Jan-Lucas Gade ◽  
Carl-Johan Thore ◽  
Jonas Stålhand
Keyword(s):  
Global Solution ◽  
Branch And Bound ◽  
Clinical Data ◽  
Minimization Problem ◽  
Branch And Bound Algorithm ◽  
Stationary Points ◽  
Model Parameters ◽  
Global Optimality ◽  
Clinical Value ◽  
Non Linear

AbstractIn this study, we consider identification of parameters in a non-linear continuum-mechanical model of arteries by fitting the models response to clinical data. The fitting of the model is formulated as a constrained non-linear, non-convex least-squares minimization problem. The model parameters are directly related to the underlying physiology of arteries, and correctly identified they can be of great clinical value. The non-convexity of the minimization problem implies that incorrect parameter values, corresponding to local minima or stationary points may be found, however. Therefore, we investigate the feasibility of using a branch-and-bound algorithm to identify the parameters to global optimality. The algorithm is tested on three clinical data sets, in each case using four increasingly larger regions around a candidate global solution in the parameter space. In all cases, the candidate global solution is found already in the initialization phase when solving the original non-convex minimization problem from multiple starting points, and the remaining time is spent on increasing the lower bound on the optimal value. Although the branch-and-bound algorithm is parallelized, the overall procedure is in general very time-consuming.

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