A reduced gradient algorithm, designed for solving the two basic classes of continuous optimization problems in the field of chemical engineering - unit operations optimization and CAD of large-scale processes - is presented in this paper. A great number of bounded variables, an implicit criterion, and a set of linear or nonlinear constraints giving rise to a sparse Jacobian matrix, form the main features of these two classes of problems.
In the case of large-scale linearly constrained problems, involving several hundreds of variables, the algorithm implementation is based both on a partition of the variables and on the use of numerically stable matrix factorizations. Nonlinear constrained problems can also be the means of numerical linearization procedures. In a second article, the algorithm is illustrated by some test problems, involving numerical and chemical engineering examples.