Two-phase material balance problem with nonlinear constraints

Recieved: 04/02/2025

Accepted: 09/25/2025

Keywords: mathematical model, material balance, optimization problem, numerical solution

To cite this article

Savenkova N.P., Mokin A.Yu., Dryazhenkov A.A., Artemyeva L.A. Two-phase material balance problem with nonlinear constraints. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2026. N 1, p.47-60 https://doi.org/10.55959/MSU/0137–0782–15–2026–50–1–47–46.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Savenkova N.P. (Lomonosov Moscow State University (MSU))
Mokin A.Yu. (Lomonosov Moscow State University (MSU))
Dryazhenkov A.A. (Lomonosov Moscow State University (MSU))
(Moscow Center for Fundamental and Applied Mathematics)
Artemyeva L.A. (Lomonosov Moscow State University (MSU))
(Moscow Center for Fundamental and Applied Mathematics)

Abstract

A nonlinear two-phase mathematical model of production at a mining plant is proposed, where ore flow is represented as two phases connected to each other through concentration of useful substance contained in the ore. The process of material balancing is studied, which leads to optimization problem with nonlinear constraints. The interior point method is used to solve the problem. Known measured values of useful substance concentrations are taken into account, as well as the results of indirect measurements, ranges of flow values, unknown concentration values, limits on stored resources. Test experiments are performed, and calculation results are demonstrated.