An interior point method for nonlinear optimization with a quasi-tangential subproblem

We present an interior point method for nonlinear programming in this paper. This method follows Byrd and Omojokun's idea of step decomposition, which splits the trial step into a normal step and a tangential step. The method employs a new idea of quasi-tangential subproblem, which is used to generate a tangential step that does not lie strictly on the tangent space of the constraints. Quasi-tangential subproblem is finally formulated into an unconstrained quadratic problem by penalizing the constraints. This method is different and maybe simpler than similar ideas, for example, the relaxed tangential step in trust funnel methods (Gould and Toint, 2010; Curtis, et al., 2017). Also, our method does not need to compute a base of the null space. A line search trust-funnel-like strategy is used to globalize the algorithm. Global convergence theorem is presented and applications to mathematical programs with equilibrium constraints are given.