An algorithm for linearly constrained programs with a partly linear objective function

A Newton-type algorithm for finding a minimum of a function, subject to linear constraints, which is linear in some of its arguments is presented. It employs an active set strategy especially adapted to this kind of problem. Compared with other methods, it is particularly efficient for problems in which the number of nonlinear variables greatly exceeds the number of linear constraints, and for which the Hessian matrix of the nonlinear part can be easily inverted. This is exemplified for the calculation of complex chemical equilibria involving an ideal gas phase with many species and pure condensed phases.