projected-search methods for bound-constrained optimization are based on performing a search along a piecewise-linear continuous path obtained by projecting a search direction onto the feasible region. a potential benefit of a projected-search method is that the direction of the search path may change multiple times at the cost of computing a single direction.
in this talk, we present a new interior method for general nonlinearly constrained optimization that combines a shifted primal-dual interior method with a projected-search method for bound-constrained optimization. the method is based on the formulation of a primal-dual penalty-barrier function that incorporates shifts on both primal and dual variables.  a modified newton direction is used in conjunction with a new projected-search algorithm that employs a non-monotone flexible quasi-armijo line search for the minimization of the penalty-barrier function. computational results indicate that the proposed method requires fewer iterations than a conventional interior method, thereby reducing the number of times that the search direction need be computed.