PRIMAL-DUAL INTERIOR METHODS FOR NONCONVEX NONLINEAR-PROGRAMMING

This paper concerns large-scale general (nonconvex) nonlinear programm ing 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 pa rameterized by a scalar parameter. The objective function of each unco nstrained subproblem is an augmented penalty-barrier function that inv olves 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 augmen ted penalty-barrier function may be interpreted as a merit function fo r values of the primal and dual variables. An inertia-controlling symm etric indefinite factorization is used to provide descent directions a nd directions of negative curvature for the augmented penalty-barrier merit function. A method suitable for large problems can be obtained b y providing a version of this factorization that will treat large spar se indefinite systems.