On the Fitting of Generalized Linear Models with Nonnegativity Parameter Constraints

We consider the problem of finding maximum likelihood estimates of a generalized linear model when some or all of the regression parameters are constrained to be nonnegative. The Kuhn-Tucker conditions of nonlinear programming can be used to characterize the solution of this constrained estimation problem when the maximum likelihood estimates exist and are unique. For the case of a generalized linear model with nonnegativity parameter constraints, the Kuhn-Tucker conditions are derived and utilized to provide a stopping rule for search algorithms for the constrained maximum likelihood estimates. Two examples are discussed.