TY - JOUR
T1 - New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation
AU - Alkhalifa, Loay
AU - Mittelmann, Hans
N1 - Funding Information:
Acknowledgments: The researchers would like to thank the Deanship of Scientific Research, Qassim University for funding publication of this project.
Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers. It would be useful if these solvers could handle mixed integer nonlinear programming (MINLP) problems. Piecewise linear approximation (PLA) is one of most popular methods used to transform nonlinear problems into linear ones. This paper will introduce PLA with brief a background and literature review, followed by describing our contribution before presenting the results of computational experiments and our findings. The goals of this paper are (a) improving PLA models by using nonuniform domain partitioning, and (b) proposing an idea of applying PLA partially on MINLP problems, making them easier to handle. The computational experiments were done using quadratically constrained quadratic programming (QCQP) and MIQCQP and they showed that problems under PLA with nonuniform partition resulted in more accurate solutions and required less time compared to PLA with uniform partition.
AB - Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers. It would be useful if these solvers could handle mixed integer nonlinear programming (MINLP) problems. Piecewise linear approximation (PLA) is one of most popular methods used to transform nonlinear problems into linear ones. This paper will introduce PLA with brief a background and literature review, followed by describing our contribution before presenting the results of computational experiments and our findings. The goals of this paper are (a) improving PLA models by using nonuniform domain partitioning, and (b) proposing an idea of applying PLA partially on MINLP problems, making them easier to handle. The computational experiments were done using quadratically constrained quadratic programming (QCQP) and MIQCQP and they showed that problems under PLA with nonuniform partition resulted in more accurate solutions and required less time compared to PLA with uniform partition.
KW - Branch and bound
KW - Mixed integer nonlinear programming
KW - Piecewise linear approximation
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U2 - 10.3390/math10020198
DO - 10.3390/math10020198
M3 - Article
AN - SCOPUS:85122493786
SN - 2227-7390
VL - 10
JO - Mathematics
JF - Mathematics
IS - 2
M1 - 198
ER -