Primal-dual interior methods for nonconvex nonlinear programming. (English) Zbl 0915.90236
Summary: 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 variables.
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.
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.
MSC:
90C30 | Nonlinear programming |
65K05 | Numerical mathematical programming methods |
49M37 | Numerical methods based on nonlinear programming |
65F05 | Direct numerical methods for linear systems and matrix inversion |
90C06 | Large-scale problems in mathematical programming |
90C26 | Nonconvex programming, global optimization |