## Primal-dual interior methods for nonconvex nonlinear programming (1998)

Venue: | SIAM Journal on Optimization |

Citations: | 59 - 5 self |

### BibTeX

@ARTICLE{Forsgren98primal-dualinterior,

author = {Anders Forsgren and Philip and E. Gill},

title = {Primal-dual interior methods for nonconvex nonlinear programming},

journal = {SIAM Journal on Optimization},

year = {1998},

volume = {8},

pages = {1132--1152}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. 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.