A practical anti-cycling procedure for linearly constrained optimization
作者： Philip E. Gill , Walter Murray , Michael A. Saunders , Margaret H. Wright
DOI: 10.1007/BF01589114
关键词: Constrained optimization 、 Linear programming 、 Numerical analysis 、 Set (abstract data type) 、 Simplex algorithm 、 Mathematics 、 Mathematical optimization 、 Sequence 、 Degeneracy (mathematics) 、 Reliability (computer networking)
摘要: A procedure is described for preventing cycling in active-set methods linearly constrained optimization, including the simplex method. The key ideas are a limited acceptance of infeasibilities all variables, and maintenance “working” feasibility tolerance that increases over long sequence iterations. additional work per iteration nominal, “stalling” cannot occur with exact arithmetic. method appears to be reliable, based on computational results first 53 linear programming problems theNetlib set.
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sci-hub.se 参考文章(35)
Edward S. Klotz, Dynamic Pricing Criteria in Linear Programming Defense Technical Information Center. ,(1988) , 10.21236/ADA198945
J C Falkner, D M Ryan, ASPECTS OF BUS CREW SCHEDULING USING A SET PARTITIONING MODEL. FROM THE BOOK COMPUTER-AIDED TRANSIT SCHEDULING ,(1988)
Julie Carolyn Falkner, Bus crew scheduling and the set partitioning model ResearchSpace@Auckland. ,(1988)
P.E. Gill, M.H. Wright, Saunders, S.J. Hammarling, W. Murray, Fortran package for constrained linear least-squares and convex quadratic programming. User's Guide for LSSOL (Version 1. 0) ,(1986)
J. L. Nazareth, Computer solution of linear programs ,(1987)
B. A. Murtagh, M. A. Saunders, MINOS 5. 0 user's guide Defense Technical Information Center. ,(1983) , 10.21236/ADA138522
J. C. Falkner, D. M. Ryan, Aspects of Bus Crew Scheduling Using a Set Partitioning Model Computer-Aided Transit Scheduling. pp. 91- 103 ,(1988) , 10.1007/978-3-642-85966-3_9
William Orchard-Hays, Advanced Linear-Programming Computing Techniques ,(1968)
George Dantzig, Alexander Orden, Philip Wolfe, THE GENERALIZED SIMPLEX METHOD FOR MINIMIZING A LINEAR FORM UNDER LINEAR INEQUALITY RESTRAINTS Pacific Journal of Mathematics. ,vol. 5, pp. 183- 195 ,(1955) , 10.2140/PJM.1955.5.183
R. FLETCHER, M. P. JACKSON, Minimization of a Quadratic Function of Many Variables Subject only to Lower and Upper Bounds Ima Journal of Applied Mathematics. ,vol. 14, pp. 159- 174 ,(1974) , 10.1093/IMAMAT/14.2.159