Abstract
In this paper, a smoothing QP-free infeasible method is proposed for nonlinear inequality constrained optimization problems. This iterative method is based on the solution of nonlinear equations which is obtained by the multipliers and the smoothing Fisher-Burmeister function for the KKT first-order optimality conditions. Comparing with other QP-free methods, this method does not request the strict feasibility of iteration. In particular, this method is implementable and globally convergent without assuming the strict complementarity condition and the isolatedness of accumulation points. Furthermore, the gradients of active constraints are not requested to be linearly independent. Preliminary numerical results indicate that this smoothing QP-free infeasible method is quite promising.
Similar content being viewed by others
References
Boggs P T, Tolle J W. Sequential quadratic programming, Acta Numerica, 1995, 45: 1–51.
Burke J V, Han S P. A robust sequential quadratic programming method, Math Programming, 1989, 43: 227–303.
De J F A, Pantoja O, Mayne D Q. Exact penalty function algorithm with simple updating of the penalty parameter, Journal of Optimization Theory and Applications, 1991, 69:441–467.
Panier E R, Tits A L, Herskovits J N. A QP-free, globally, locally superlinear convergent method for the inequality constrained optimization problems, SIAM J Control Optim, 1988, 36: 788–811.
Qi H, Qi L. A new QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization, SIAM J Optim, 2000, 11: 113–132.
Fischer A. A special Newton-type optimization method, Optimization, 1992, 24: 269–284.
Pu D, Zhou Y, Zhang H. A QP-free feasible method, J Comput Math, 2004, 22: 651–660.
Qi L, Sun D, Zhou G. A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities, Math Prog, 2000, 87: 1–35.
Pu D, Zhang J. An inexact generalized Newton method for second order C-differentiable optimization, J Comput Appl Math, 1998, 93: 107–122.
Hock W, Schittkowski K. Test example for nonlinear programming Codes, Lecture Notes in Econom and Math Systems 187, Berlin: Springer-Verlag, 1981.
Author information
Authors and Affiliations
Additional information
Supported by the National Natural Science Foundation of China(10371089) and the Foundation of Qingdao University.
Rights and permissions
About this article
Cite this article
Zhou, Y., Pu, D. A smoothing QP-free infeasible method for nonlinear inequality constrained optimization. Appl. Math.- J. Chin. Univ. 22, 425–433 (2007). https://doi.org/10.1007/s11766-007-0407-y
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11766-007-0407-y