Feasibility Restore Phase
The feasibility restore phase [9] aims at finding a new iterate acceptable to the current filter by reducing the constraints violation. It is intuitively formulated as an optimization problem to find a feasible point being the closest to the current point:
 (30)
where  is a diagonal scaling matrix whose elements are
 (31)
Since the objective is a positive definite quadratic function, the optimal solution to problem (30) is usually a strict local minimum in the manifold defined by the equality constraints of (30), which makes problem (30) relatively easier to solve. The augmented Lagrangian Method [12] with projected Newton steps [13] is applied to solve this problem in this paper.
The algorithm terminates and reverts to regular IPM iterations once an acceptable point is obtained.
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