Global Convergence Analysis of Algorithms for Finding Feasible Points in Norm-Relaxed MFD

This paper introduces two new algorithms for finding initial feasible points from initial infeasible points for the recently developed norm-relaxed method of feasible directions (MFD). Their global convergence is analyzed. The theoretical results show that both methods are globally convergent; one of them guarantees finding a feasible point in a finite number of steps. These two methods are very convenient to implement in the norm-relaxed MFD. Numerical experiments are carried out to demonstrate their performance on some classical test problems and to compare them with the traditional method of phase I problems. The numerical results show that the methods proposed in this paper are more effective than the method of phase I problems in the norm-relaxed MFD. Hence, they can be used for finding initial feasible points for other MFD algorithms and other nonlinear programming methods.

[1]  M. M. Kostreva,et al.  Generalization of Murty's direct algorithm to linear and convex quadratic programming , 1989 .

[2]  A. F. Veinott,et al.  On the Convergence of Some Feasible Direction Algorithms for Nonlinear Programming , 1967 .

[3]  M. M. Kostreva,et al.  Self-Tuning Norm-Relaxed Method of Feasible Directions , 1997 .

[4]  D. Mayne,et al.  An efficient algorithm for solving inequalities , 1985 .

[5]  Klaus Schittkowski,et al.  More test examples for nonlinear programming codes , 1981 .

[6]  Garret N. Vanderplaats,et al.  Numerical optimization techniques for engineering design , 1999 .

[7]  E. Polak,et al.  Rate of Convergence of a Class of Methods of Feasible Directions , 1973 .

[8]  G. Vanderplaats An efficient feasible directions algorithm for design synthesis , 1984 .

[9]  G. Zoutendijk,et al.  Methods of Feasible Directions , 1962, The Mathematical Gazette.

[10]  M. Kostreva,et al.  Norm-relaxed method of feasible directions for solving nonlinear programming problems , 1994 .

[11]  J. Korycki,et al.  A norm-relaxed method of feasible directions (MFD) for solving nonlinear programming problems , 1996 .

[12]  Jasbir S. Arora,et al.  Methods for finding feasible points in constrained optimization , 1995 .

[13]  Hector A. Rosales-Macedo Nonlinear Programming: Theory and Algorithms (2nd Edition) , 1993 .

[14]  Surya N. Patnaik,et al.  An optimization algorithm based on the method of feasible directions , 1995 .

[15]  J. Korycki,et al.  Norm-relaxed method of feasible directions: application in structural optimization , 1996 .

[16]  Elijah Polak,et al.  Computational methods in optimization , 1971 .

[17]  Jack A. Korycki,et al.  Norm-Relaxed Method of Feasible Directions , 1995 .

[18]  M. M. Kostreva,et al.  Convergence analysis of norm-relaxed method of feasible directions , 1996 .

[19]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .