Partial Linearization Methods in Nonlinear Programming 1

In this paper, we characterize a class of feasible direction methods in nonlinear programming through the concept of partial linearization of the objective function. Based on a feasible point, the objective is replaced by an arbitrary convex and continuously diierentiable function, and the error is taken into account by a rst order approximation of it. A new feasible point is deened through a line search with respect to the original objective, towards the solution of the approximate problem. Global convergence results are given for exact and approximate line searches, and possible interpretations are made. We present some instances of the general algorithm, and discuss extensions to nondiierentiable programming.