A Generalized Variational Optimization Framework for Industrial Process Management

Abstract

The paper presents a generalized variational optimization framework that allows managing complex industrial processes by representing process decisions as functionals within a convex functional space rather than scalar variables. In the proposed technique, the optimization problem of the industrial system is represented in a form of variational inequality model in which the optimal state is represented by the equilibrium between multiple process goals and constraints along with the interrelations. Using the operator theory, the mathematical properties of the optimal equilibrium in terms of existence, uniqueness, convergence, and stability are determined with the help of monotone operators and fixed-point theory. An algorithm using projections is constructed for solving the equilibrium problem while maintaining feasibility despite system constraints. The efficiency of the proposed framework is evaluated based on the results of numerical experiments carried out on examples of industrial optimization problems. It has been found that the proposed framework ensures faster convergence, lower equilibrium error, better constraint satisfaction, and higher operator stability compared to classical gradient and convex optimization techniques.