QP-Free Method for Nonlinear Programming Problems
In this paper, A QP-free feasible method was proposed to obtain the local convergence under some weaker conditions for the minimization of a smooth function subject to smooth inequalities. Based on the solutions of linear systems of equation reformulation of the KKT optimality conditions, this method uses the 3-1 NCP function.The method is iterative, which means each iteration can be viewed as a perturbation of a Newton or Quasi Newton on both the primal and dual variables for the solution of the equalities in the KKT first order conditions of optimality, and the feasibility of all iterations is ensured in this method. In particular, this method is implementable and globally convergent without assuming the strict complementarity condition, the isolation of the accumulation point and the linear independence of the gradients of active constrained functions. The method has also superlinear convergence rate under some mild conditions.
A. P. Jiang and F. W. Huang, "QP-Free Method for Nonlinear Programming Problems", Key Engineering Materials, Vols. 467-469, pp. 882-887, 2011