*(French)*Zbl 0571.90055

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.

##### MSC:

90C06 | Large-scale problems (mathematical programming) |

90C30 | Nonlinear programming |

65K05 | Mathematical programming (numerical methods) |

90C90 | Applications of mathematical programming |