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

Authors: Matthew West Joseph Zilvar

Addresses: Department of Industrial and Manufacturing Engineering, California State Polytechnic University, 3801 West Temple Avenue, Pomona, California 91768, USA

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.

DOI: 10.1504/IJOR.2025.144671

International Journal of Operational Research, 2025 Vol.52 No.3, pp.334 - 359

Received: 03 Dec 2021
Accepted: 28 Jun 2022
Published online: 27 Feb 2025 *

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