A generalization of the norm-relaxed method of feasible directions

Applied Mathematics and Computation - Tập 102 - Trang 257-272 - 1999
X.B. Chen1, M.M. Kostreva1
1Department of Mathematical Sciences, Clemson University, Clemson, NC 29634-1907, USA

Tài liệu tham khảo

Belegundu, 1995, An optimization algorithm based on the method of feasible directions, Struct. Optimiz., 9, 83, 10.1007/BF01758824 G.N. Vanderplaats, Numerical Optimization Techniques for Engineering Design, McGraw-Hill, New York, 1984 Vanderplaats, 1984, Efficient feasible directions algorithm for design synthesis, AIAA J., 22, 1633, 10.2514/3.8829 G.N. Vanderplaats, DOT/DOC Users Manual, Vanderplaats, Miura and Associates, 1993 E. Polak, Computational Methods in Optimization, Academic Press, New York, 1971 G. Zoutendijk, Methods of Feasible Directions, Elsevier, Amsterdam, 1960 P. Wolfe, On the convergence of gradient methods under constraints, IBM Research Report RC 1752, Yorktown Heights, New York, 1967 Topkis, 1967, On the convergence of some feasible direction algorithms for nonlinear programming, SIAM J. Control, 5, 268, 10.1137/0305018 Pironneau, 1972, On the rate of convergence of certain methods of centers, Math. Program., 2, 230, 10.1007/BF01584544 Pironneau, 1973, Rate of convergence of a class of methods of feasible directions, SIAM J. Num. Anal., 10, 161, 10.1137/0710017 Chaney, 1976, On the Pironneau–Polak method of centers, J. Optimiz. Theory Applications, 20, 269, 10.1007/BF00933624 Chaney, 1976, On the rate of convergence of some feasible direction algorithm, J. Optimiz. Theory Applications, 20, 297, 10.1007/BF00933625 Wiest, 1992, A generalized quadratic programming-based phase I–phase II method for inequality constrained optimization, J. Appl. Math. and Optimiz., 26, 223, 10.1007/BF01371083 Polak, 1979, Combined phase I–phase II methods of feasible directions, Math. Program., 17, 61, 10.1007/BF01588225 Herskovits, 1986, A two-stage feasible directions algorithm for nonlinear constrained optimization, Math. Program., 36, 19, 10.1007/BF02591987 Cawood, 1994, Norm-relaxed method of feasible directions for solving nonlinear programming problems, J. Optimiz. Theory Applications, 83, 311, 10.1007/BF02190059 J.A. Korycki, Norm-relaxed method of feasible directions, Ph.D. Dissertation, Department of Mathematical Sciences, Clemson University (1995) Korycki, 1996, Convergence analysis of norm-relaxed method of feasible directions, J. Optimiz. Theory Applications, 91, 389, 10.1007/BF02190102 Korycki, 1996, Norm-relaxed method of feasible directions: Application in structural optimization, Struct. Optimiz., 11, 187, 10.1007/BF01197034 Korycki, 1997, Self-tuning norm-relaxed method of feasible directions, J. Optimiz. Theory Applications, 92, 311, 10.1023/A:1022655129695 Kostreva, 1989, Generalization of Murty's direct algorithm to linear and convex quadratic programming, J. Optimiz. Theory Applications, 62, 63, 10.1007/BF00939630 M.M. Kostreva, X.B. Chen, J.A. Korycki, A norm-relaxed method of feasible directions for solving nonlinear programming problems, in: Proc. Sixth AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Bellevue, WA, September 1996 M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming: Theory and Algorithms, second edition, Wiley, 1993 W. Hock, K. Schittkowski, Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, vol. 187, Springer, Berlin, 1981 K. Schittkowski, More Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, vol. 282, Springer, Berlin, 1987