Sequential Bound Constrained Minimization Technique for Large-scale Process System Optimization

Based on sequential unconstrained programming method, the sequential bound constrained programming algorithms for large-scale process system optimization are studied in this paper. Since mild variables are introduced according to all inequality constraints, the penalty function of our algorithms only constraints the penalty terms for equality constraints. A series of bound constrained sub-problems instead of a series of unconstrained sub-problems are solved in these algorithms. The sequential bound constrained programming algorithms are performed in two stages. The inner stage is the bound constrained minimization of the argumented Lagrange penalty function in which a new set of primal variables is found. The outer stage is performed to update the Lagrange multipliers and penalty parameters, check for convergence and accordingly reinitiate another bound constrained minimization or declare convergence. Further more, a modified truncated-Newton algorithm is proposed to solve the bound constrained sub-problems. Finally, numerical experiments are made for two kinds of alterable dimension nonlinear programming problems, which proves the stability and effectiveness of the algorithms for large-scale process system optimization.