BibTeX
@ARTICLE{
         Walther2012Afo,
       author = "Walther, Andrea and Vetukuri, Rama Raju and Biegler, Lorenz T.",
       title = "A first-order convergence analysis of trust-region methods with inexact {J}acobians
         and inequality constraints",
       journal = "Optimization Methods and Software",
       volume = "27",
       number = "2",
       pages = "373--389",
       year = "2012",
       doi = "10.1080/10556788.2011.606574",
       url = "http://www.tandfonline.com/doi/abs/10.1080/10556788.2011.606574",
       eprint = "http://www.tandfonline.com/doi/pdf/10.1080/10556788.2011.606574",
       abstract = "A class of trust-region algorithms is developed and analyzed for the solution of
         minimization problems with nonlinear inequality constraints. Based on composite-step trust-region
         methods with barrier functions, the resulting algorithm also does not require the computation of
         exact Jacobians; only Jacobian vector products are used along with approximate Jacobian matrices.
         Therefore, the proposed method is targeted on small or medium size problems with dense Jacobians of
         the constraints. As demonstrated on small numerical examples, this feature has significant potential
         benefits for problems where Jacobian calculations are expensive.",
       ad_area = "Optimization"
}