Paper Info
Title
Mathematical programming formulations for piecewise polynomial functions
Abstract
This paper studies mathematical programming formulations for solving optimization problems with piecewise polynomial (PWP) constraints. We elaborate on suitable polynomial bases as a means of efficiently representing PWPs in mathematical programs, comparing and drawing connections between the monomial basis, the Bernstein basis, and B-splines. The theory is presented for both continuous and semi-continuous PWPs. Using a disjunctive formulation, we then exploit the characteristic of common polynomial basis functions to significantly reduce the number of nonlinearities, and to suggest a bound-tightening technique for PWP constraints. We derive several extensions using Bernstein cuts, an expanded Bernstein basis, and an expanded monomial basis, which upon a standard big-M reformulation yield a set of new MINLP models. The formulations are compared by globally solving six test sets of MINLPs and a realistic petroleum production optimization problem. The proposed framework shows promising numerical performance and facilitates the solution of PWP-constrained optimization problems using standard MINLP software.
Year
DOI
Venue
2020
10.1007/s10898-020-00881-4
Journal of Global Optimization
Keywords
DocType
Volume
Piecewise polynomials, Splines, Mixed integer programming, Nonlinear programming, Disjunctions
Journal
77
Issue
ISSN
Citations 
3
0925-5001
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Bjarne Grimstad100.34
Brage R. Knudsen200.34