A null-space primal-dual interior-point algorithm for nonlinear optimization with nice convergence properties (Q1960196)

A primal-dual interior-point algorithm for the solution of general nonlinear optimization problems with inequality and equality constraints is presented and its convergence properties are studied. The algorithm consists of the approximate solution of a sequence of minimization problems which have the logarithmic barrier function with a given barrier parameter as objective function and contain equality constraints. In each iteration a range-space and a null-space step is computed, and the \(\ell_2\) penalty function is used as the merit function. Under mild conditions, which do not include any regularity assumption, strong global convergence results can be proved for the inner algorithm as well as for a combined outer and inner algorithm. It is furthermore shown that, under suitable control of the exactness of range-space steps and of the selection of the penalty parameter and Hessian approximation, the algorithm locally generates superlinearly or quadratically convergent steps.