Review Questions 539
interpretation, pp. 15–21, inProgress in Engineering Optimization–1981, R. W. Mayne
and K. M. Ragsdell, Eds., ASME, New York, 1981.
8.31 M. Avriel, R. Dembo, and U. Passey, Solution of generalized geometric programs,Inter-
national Journal for Numerical Methods in Engineering, Vol. 9, pp. 149–168, 1975.
8.32 Computational aspects of geometric programming: 1. Introduction and basic notation,
pp. 115–120 (A. B. Templeman), 2. Polynomial programming, pp. 121–145 (J. Bradley),
- Some primal and dual algorithms for posynomial and signomial geometric programs,
pp. 147–160 ( J. G. Ecker, W. Gochet, and Y. Smeers), 4. Computational experiments in
geometric programming, pp. 161–173 ( R. S. Dembo and M. J. Rijckaert),Engineering
Optimization, Vol. 3, No. 3, 1978.
8.33 A. J. Morris, Structural optimization by geometric programming,International Journal
of Solids and Structures, Vol. 8, pp. 847–864, 1972.
8.34 A. J. Morris, The optimisation of statically indeterminate structures by means of approx-
imate geometric programming, pp. 6.1–6.17in Proceedings of the 2nd Symposium on
Structural Optimization, AGARD Conference Proceedings 123, Milan, 1973.
8.35 A. B. Templeman and S. K. Winterbottom, Structural design applications of geometric pro-
gramming, pp. 5.1–5.15in Proceedings of the 2nd Symposium on Structural Optimization,
AGARD Conference Proceedings 123, Milan, 1973.
8.36 A. B. Templeman, Structural design for minimum cost using the method of geomet-
ric programming, Proceedings of the Institute of Civil Engineers, London, Vol. 46,
pp. 459–472, 1970.
8.37 J. E. Shigley and C. R. Mischke,Mechanical Engineering Design, 5th ed., McGraw-Hill,
New York, 1989.
Review Questions
8.1 State whether each of the following functions is a polynomial, posynomial, or both.
(a)f= 4 −x 12 + 6 x 1 x 2 + 3 x^22
(b)f= 4 + 2 x 12 + 5 x 1 x 2 +x 22
(c)f= 4 + 2 x 12 x 2 −^1 + 3 x 2 −^4 + 5 x 1 −^1 x^32
8.2 Answer true or false:
(a)The optimum values of the design variables are to be known before finding the
optimum value of the objective function in geometric programming.
(b)∗jdenotes the relative contribution of thejth term to the optimum value of the
objective function.
(c)There are as many orthogonality conditions as there are design variables in a geometric
programming problem.
(d)Iffis the primal andvis the dual,f≤v.
(e)The degree of difficulty of a complementary geometric programming problem is given
by (N−n−1), wherendenotes the number of design variables andNrepresents the
total number of terms appearing in the numerators of the rational functions involved.
(f)In a geometric programming problem, there are no restrictions on the number of
design variables and the number of posynomial terms.
8.3 How is the degree of difficulty defined for a constrained geometric programming problem?
8.4 What is arithmetic–geometric inequality?
