1. Examples of optimization problems

1.1 Calculating a chemical equilibrium

Consider the system formed by the mixture of a number of chemical elements (for example, three elements: sulfur, oxygen and fluorine). Under given conditions of pressure P and thermodynamic temperature T, an equilibrium is established between these elements and all the compounds they are likely to form (here there are 35 possible chemical bodies: SO ₂ , SF ₂ , etc.). We wish to calculate the concentrations of the various constituents at equilibrium. To do this, we express that at equilibrium the energy of the system is minimal.

• Mathematical model

This problem illustrates the...