Primal-Dual Interior Methods For Nonconvex Nonlinear Programming
Anders Forsgren and Philip E. Gill
This paper concerns large-scale general (nonconvex) nonlinear
programming when first and second derivatives of the objective and
constraint functions are available. A method is proposed that is
based on finding an approximate solution of a sequence of
unconstrained subproblems parameterized by a scalar parameter. The
objective function of each unconstrained subproblem is an augmented
penalty-barrier function that involves both primal and dual variables.
Each subproblem is solved with a modified Newton method that generates
search directions from a primal-dual system similar to that proposed
for interior methods. The augmented penalty-barrier function may be
interpreted as a merit function for values of the primal and dual
An inertia-controlling symmetric indefinite factorization is used to
provide descent directions and directions of negative curvature for
the augmented penalty-barrier merit function. A method suitable for
large problems can be obtained by providing a version of this
factorization that will treat large sparse indefinite systems.
SIAM Journal on Optimization 8 (1998), 1132-1152.