A study of filter method for solving non-linear problems

Document Type : Research Paper

Author

Department of Mathematics, University of Isfahan

Abstract

One of methods for solving nonlinear programming problems that has been used for years is Penalty method. In this paper we introduce a new concept that is Filter, then we expressed algorithm for solving nonlinear constrained programming problems so that the Penalty function is not used. If we uses the algorithm of the Filter instead of the Penalty function, them some of the problems of the penalty method are solved and also the global convergence will be implied.

Keywords


 [1] R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function, Math. Program., 91 (2002) 239–269.
[2] R. Fletcher, S. Leyffer and P. L. Toint, On the global convergence of a filter-SQP algorithm,
SIAM J. Optim., 13 (2002) 44–59.
[3] X. Zhu and D. Pu, A line search filter algorithm with inexact step computations for equality constrained optimization,
Appl. Num. Math., 62 (2012) 212-223.
[4] J. Nocedal and S. J. Wright,
Numerical Optimization, 2nd ed., Springer, New York, 2006.
[5] W. Hock and K. Schittkowski,
Test Example for nonlinear programming codes, Springer-Verlag, Berlin-New York, 1981.