Partial Linearization Methods in Nonlinear Programming

M. Patriksson
Department of Mathematics
Linköping Institute of Technology
Linköping, Sweden

ABSTRACT:

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
differentiable function, and the error is taken into account by a first 
order approximation of it. A new feasible point is defined 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 nondifferentiable programming.

KEY WORDS: Feasible Direction Methods, Partial Linearization, Regularization, 
Nondifferentiable Programming