Linearisation of nonlinear programs using the essence of calculus and integer programming

Matthew West Joseph Zilvar

International Journal of Operational Research, 2025, vol. 52, issue 3, 334-359

Abstract: This paper contains an approach to solve nonlinear programming (NLP) problems using a linearisation approach based on theorems of calculus. The solution method relies upon dividing functions with finite domains into a series of domains and coefficients used to model linear and nonlinear functions within a mixed integer linear program (MILP). Nonlinear terms are solved for in the objective function and constraints while achieving global optimality at a specified resolution using the international system of units (SI). An efficient solution method is provided by creating a set of MILPs that represent the same problem with different complexities and using the solutions to achieve global optimality. Numerical results and a comparison are provided. From the results an argument in the P versus NP problem is formed.

Keywords: linearisation; nonlinear programming; integer programming; P vs. NP; calculus; logarithmic programming; transportation problem; set forming; complexity theory; global optimality; mixed integer linear program; MILP. (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.inderscience.com/link.php?id=144671 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ids:ijores:v:52:y:2025:i:3:p:334-359

Access Statistics for this article

More articles in International Journal of Operational Research from Inderscience Enterprises Ltd
Bibliographic data for series maintained by Sarah Parker ().