Generalization of dual structural optimization problems in terms of fractional programming
Author:
A. J. Morris
Journal:
Quart. Appl. Math. 36 (1978), 115-119
MSC:
Primary 90C30
DOI:
https://doi.org/10.1090/qam/496698
MathSciNet review:
496698
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: Duality now plays an important role in the theory of optimum structures but has not been given adequate detailed consideration within this context. The paper makes a limited attempt to satisfy this requirement through a generalization of the associated duality theory by formulating the structural optimization as a fractional program. This provides some new forms for the dual objective function and crystalizes some of the intrinsic problems associated with dual structural programs.
W. S. Hemp, Optimum structures, Oxford, 1973
P. Bartholomew and A. J. Morris, A unified approach to fully-stressed design, Eng. Optimisation 2, 3–15 (1976)
A. B. Templeman, A dual approach to optimum stress design, J. Struct. Mech. 4, 235–257 (1976)
P. Bartholomew, A dual bound used for monitoring structural optimisation programs, Eng. Optimization, to appear
Olvi Mangasarian, Non-linear programming, McGraw-Hill, 1969
R. Jagannathan, Duality in non-linear fractional programming, Z. Operations Research 17, 1–3 (1973)
C. R. Bector, Duality in non-linear programming, Z. Operations Research 17, 183–193 (1973)
- S. Schaible, Parameter-free convex equivalent and dual programs of fractional programming problems, Z. Operations Res. Ser. A-B 18 (1974), A187–A196 (English, with German summary). MR 351464, DOI https://doi.org/10.1007/bf02026600
- D. G. Mahajan and M. N. Vartak, Generalization of some duality theorems in nonlinear programming, Math. Programming 12 (1977), no. 3, 293–317. MR 459636, DOI https://doi.org/10.1007/BF01593799
W. S. Hemp, Optimum structures, Oxford, 1973
P. Bartholomew and A. J. Morris, A unified approach to fully-stressed design, Eng. Optimisation 2, 3–15 (1976)
A. B. Templeman, A dual approach to optimum stress design, J. Struct. Mech. 4, 235–257 (1976)
P. Bartholomew, A dual bound used for monitoring structural optimisation programs, Eng. Optimization, to appear
Olvi Mangasarian, Non-linear programming, McGraw-Hill, 1969
R. Jagannathan, Duality in non-linear fractional programming, Z. Operations Research 17, 1–3 (1973)
C. R. Bector, Duality in non-linear programming, Z. Operations Research 17, 183–193 (1973)
S. Schaible, Parameter-free convex equivalent and dual programs of fractional programming problems, Z. Operations Research 18, 187–196 (1974)
D. G. Mahajan and M. N. Vartak, Generalisation of some duality theorems in non-linear programming, Mathematical Programming 12, 293–317 (1977)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
90C30
Retrieve articles in all journals
with MSC:
90C30
Additional Information
Article copyright:
© Copyright 1978
American Mathematical Society
