Solving generalized polynomial problem by using new affine relaxed technique

Abstract

This article presents and validates a new branch-and-bound algorithm for effectively solving the generalized polynomial problem (GPP). In this algorithm, a new affine relaxed technique is derived for establishing the relaxed linear programs problem of the GPP. In addition, some box reducing manipulations are employed to improve the speed of branch-and-bound search of the algorithm. Combining the relaxed linear programs problem with the box reducing manipulations, a new branch-and-bound algorithm is constructed. Some numerical examples are solved to verify the potential practical and computing advantages of the algorithm. At last, several engineering design problems are solved to validate the usefulness of the algorithm.

Keywords:

• Generalized polynomial problem
• fractional programming
• global optimization
• affine relaxed technique
• branch-and-bound

2010 Mathematics Subject Classifications:

• 90C26
• 90C32
• 65K05

Acknowledgments

This paper is supported by the National Natural Science Foundation of China (11871196, 12071133, 12071112), the China Postdoctoral Science Foundation (2017M622340), the Higher School Key Scientific Research Projects of Henan Province (18A110019, 17A110021), the Key Scientific and Technological Research Projects of Henan Province (202102210147, 192102210114), the Science and Technology Climbing Program of Henan Institute of Science and Technology (2018JY01), Henan Institute of Science and Technology Postdoctoral Science Foundation.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper is supported by the National Natural Science Foundation of China [11871196, 12071133, 12071112], the China Postdoctoral Science Foundation [2017M622340], the Higher School Key Scientific Research Projects of Henan Province [18A110019, 17A110021], the Key Scientific and Technological Research Projects of Henan Province [202102210147, 192102210114], the Science and Technology Climbing Program of Henan Institute of Science and Technology [2018JY01], Henan Institute of Science and Technology Postdoctoral Science Foundation.