COMPARISON OF SOFTWARE IMPLEMENTATIONS OF THE METHOD OF UNCERTAIN LAGRANGE MULTIPLIERS AND THE METHOD OF PENALTY FUNCTIONS IN SOLVING THE PROBLEM OF DETERMINING THE EQUILIBRIUM COMPOSITION USING THE EXAMPLE OF THE C-O SYSTEM

Background. The problem of finding the equilibrium composition of a complex multicomponent system is accomplished by determining the minimum of the reduced Gibbs energy under constraints associated with taking into account the mass balance. Materials and methods. The choice of methods for transition from a conditional optimization problem to an unconditional optimization problem is considered. The methods of undetermined Lagrange multipliers and the penalty function method with different parameters were compared. The choice of the method for transition from the unconditional optimization problem to the conditional optimization problem affected the form of the objective function of the reduced Gibbs energy. Results. When changing the objective function, it was necessary to modify the algorithm for determining the first and second derivatives in the Newton – Raphson method, which is used to solve a system of nonlinear algebraic equations. Conclusions. A comparative analysis of two software implementations of the penalty function method is carried out: with a constant penalty value and with a monotonically increasing penalty value, and the Lagrange multiplier method.