Sequential Bound Constrained Minimization Method for Solving Complex Process System Optimization Problems

Steady-state optimization of complex process systems in engineering practice is a typical class of large-scale optimization problems. In this paper, we propose a new method, Sequential Bound Constrained Minimization (SBCM) method, for solving such optimization problems. Specifically, by introducing relaxation variables properly into engineering optimization model, the derived penalty function encompasses only penalty items related to equality constraints, excluding those pertaining to bound and inequality constraints. The solution to the original optimization problem is obtained through solving a series of bound constrained subproblems instead of a series of unconstrained subproblems. Furthermore, a modified truncated-Newton method is provided to solve the bound constrained subproblems. Finally, numerical simulations are conducted on two nonlinear optimization problems with varying dimensions and the simulation results demonstrate the stability and effectiveness of the proposed method.