Computational Comparison of Piecewise−Linear Relaxations for Pooling Problems

2009 ◽  
Vol 48 (12) ◽  
pp. 5742-5766 ◽  
Author(s):  
Chrysanthos E. Gounaris ◽  
Ruth Misener ◽  
Christodoulos A. Floudas
Keyword(s):  
Piecewise Linear ◽  
Linear Relaxations ◽  
Computational Comparison

scholarly journals On refinement strategies for solving $${\textsc {MINLP}\mathrm{s}}$$  by piecewise linear relaxations: a generalized red refinement

2021 ◽  
Author(s):  
Robert Burlacu
Keyword(s):  
Power Flow ◽  
Optimal Power Flow ◽  
Piecewise Linear ◽  
Mixed Integer ◽  
Nonlinear Program ◽  
Convergence Conditions ◽  
Incremental Method ◽  
Optimal Power ◽  
Refinement Procedure ◽  
Linear Relaxations

AbstractWe investigate the generalized red refinement for n-dimensional simplices that dates back to Freudenthal (Ann Math 43(3):580–582, 1942) in a mixed-integer nonlinear program ($${\textsc {MINLP}}$$ MINLP ) context. We show that the red refinement meets sufficient convergence conditions for a known $${\textsc {MINLP}}$$ MINLP  solution framework that is essentially based on solving piecewise linear relaxations. In addition, we prove that applying this refinement procedure results in piecewise linear relaxations that can be modeled by the well-known incremental method established by Markowitz and Manne (Econometrica 25(1):84–110, 1957). Finally, numerical results from the field of alternating current optimal power flow demonstrate the applicability of the red refinement in such $${\textsc {MIP}}$$ MIP -based $${\textsc {MINLP}}$$ MINLP  solution frameworks.

Chaos in a manifold piecewise linear system

1981 ◽  
Vol 64 (10) ◽  
pp. 9-17 ◽  
Author(s):  
Toshimichi Saito ◽  
Hiroichi Fujita
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System
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