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

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  • Matthew West Joseph Zilvar

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.

Suggested Citation

  • Matthew West Joseph Zilvar, 2025. "Linearisation of nonlinear programs using the essence of calculus and integer programming," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 52(3), pages 334-359.
    • Handle: RePEc:ids:ijores:v:52:y:2025:i:3:p:334-359
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