swMATH ID: 
34823

Software Authors: 
BalteanLugojan, Radu; Misener, Ruth

Description: 
StdPoolingPolyAlgos: Implementation of polynomialtime algorithms for subclasses of single quality standard pooling problems. Paper: Piecewise parametric structure in the pooling problem: from sparse stronglypolynomial solutions to NPhardness. The standard pooling problem is a NPhard subclass of nonconvex quadraticallyconstrained optimization problems that commonly arises in process systems engineering applications. We take a parametric approach to uncovering topological structure and sparsity, focusing on the single quality standard pooling problem in its (p)formulation. The structure uncovered in this approach validates Professor Christodoulos A. Floudas’ intuition that pooling problems are rooted in piecewisedefined functions. We introduce dominant active topologies under relaxed flow availability to explicitly identify pooling problem sparsity and show that the sparse patterns of active topological structure are associated with a piecewise objective function. Finally, the paper explains the conditions under which sparsity vanishes and where the combinatorial complexity emerges to cross over the (P/NP) boundary. We formally present the results obtained and their derivations for various specialized single quality pooling problem subclasses. 
Homepage: 
https://link.springer.com/article/10.1007/s108980170577y

Source Code: 
https://github.com/cogimperial/StdPoolingPolyAlgos

Keywords: 
standard pooling problem;
global optimization;
piecewise structure;
sparsity;
discretization;
(P/ NP) boundary;
stronglypolynomial algorithms

Related Software: 
APOGEE;
GloMIQO;
GAMS Model;
SPOTless;
SparseBSOS;
AIMMS;
Mosek;
CONOPT;
BARON;
GitHub;
ANTIGONE;
SCIP

Cited in: 
5 Publications
