  In this paper, we proposed an interior point method for constrained
optimization, which is characterized by the using of quasi-tangential
subproblem. This algorithm follows the main ideas of primal dual interior point
methods and Byrd-Omojokun's step decomposition strategy. The quasi-tangential
subproblem is obtained by penalizing the null space constraint in the
tangential subproblem. The resulted quasi-tangential step is not strictly lying
in the null space of the gradients of constraints. We also use a line search
trust-funnel-like strategy, instead of penalty function or filter technology,
to globalize the method. Global convergence results were obtained under
standard assumptions.
