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Nonlinear Programming Final Exam

section B

Below is a list of references concerning Geometric Programming and applications. Part I lists
papers which explicity use GP, while Part II lists papers whose applications appear to be good
candidates for GP.

Part I: Selected References to
Geometric Programming Applications

56:271 Spring '97
D. Bricker
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Paul, H. (1982). “An Application of Geometric Programming to Heat Exchanger Design.”
Computers and Industrial Engineering 6(2): 103-114.

Phillips, D. T. and C. S. Beightler (1970). “Optimization in Tool Engineering Using Geometric
Programming.” AIIE Transactions 2(4): 355-360.

Corstjens, M. and P. Doyle (1981). “A Model for Optimizing Retail Space Allocations.”
Management Science 27(7): 822-833.

Balachandran, V. and D. Gensch (1973). Solving the "Marketing Mix" Problem Using Geometric
Programming. Northwestern University.

Dajani, J. S., Y. Hasit, et al. (1977). “Geometric Programming in Sewer Network Design.”
Engineering Optimization 3: 27-35.

Edwards, L. S. (1975). “Optimum Limit State Design of Highway Bridge Superstructures Using
Geometric Programming.” Engineering Optimization 1: 201-212.

Unklesbay, K. and D. L. Creighton (1978). “The Optimization of Multi-pass Machining Process.”
Engineering Optimization 3: 229-238.

Mine, H. and K. Ohno (1970). “Decomposition of Mathematical Programming Problems by
Dynamic Programming and its Application to BLock-Diagonal Geometric Programs.” J.
Jath. Anal. Appl. 32: 370ff.

Yu, C. H., N. C. Dasgupta, et al. (1986). “Optimization of Prestressed Concrete Bridge Girders.”
Engineering Optimization 10(1): 13-24.

Kapur, K. C. (1978). Optimization in Probabilistic Design for Engineering Systems . Second
International Symposium on Large Engineering Systems, Waterloo, Sandford Educational
Press .

Wyman, F. P. (1978). “Use of Geometric Programming in the Design of an Algerian Water
Conveyance System.” Interfaces 8(3): 1-6.

Philipson, R. H. and A. Ravindran (1979). “Application of Mathematical Programming to Metal
Cutting.” Mathematical Programming Study 11: 116-134.

Hivner, W. H. and R. P. Mehta (1977). “Optimizing Computer Performance with Geometric
Programming.” European Journal of Operational Research 1(2):

Grange, F. E., G. A. Kochenberger, et al. (1992). Optimal Design of Multi-Pass Heat Exchangers
with Geometric Programming.

Woolsey, R. E. D. An Analysis of a Model of the MPS MX Missile System Using Geometric
Programming. Mathematics Dept., Colorado School of Mines.

Gopalakrishnan, B. and F. Al-Khayyal (1991). “Machine Parameter Selection for Turning based
on Geometric Programming.” International Journal of Production Research 29: 1897-
1908.

Smeers, Y. and D. Tyteca (1984). “A Geometric Programming Model for the Optimal Design of
Wastewater Treatment Plants.” Operations Research 32(2): 314-342.

a. Chose one reference from Part I of the list of GP applications.

b. Briefly summarize the application problem.

c. Write the mathematical model.

d. Identify the # of (primal) variables , # of constraints, total # of terms.

e. State whether posynomial or signomial in nature .

f. Describe the method used by the author(s) of the paper.

g. If sample data is given for a sample problem, or if you can guess at reasonable data, solve
the GP problem.
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Part II: Selected References to Potential
Geometric Programming Applications

Dinkel, J. J. and G. A. Kochenberger (1974). “On "A Cofferdam Design Optimization".”
Mathematical Programming 6(1): 114-116.

Neghabat, F. and R. M. Stark (1972). “A Cofferdam Design Optimization".” Mathematical
Programming 3: 263-275.

Feiring, B. R. (1990). “An Efficient Procedure for the N-city Traveling Salesman Problem.”
Mathematical and Computer Modelling 13(3): 95-98.

Terry, W. R. and K. W. Cutright (1986). Computer Aided Design of a Broaching Process.
Computers and Industrial Engineering. 11: 576-580.

Ulusoy, A. G. and D. M. Miller (1979). Optimal Design of Pipeline Networks Carrying
Homogeneous Coal Slurry. Mathematical Programming Study. North-Holland Publishing
Company. 85-107.

Cowton, C. J. and A. Wirth (1993). “On the Economics of Cutting Tools.” International Journal
of Production Research 31(10): 2441-2446.

Quesada, I. and I. E. Grossmann (1992). A Global Optimization Algorithm for Heat Exchanger
Networks. Engineering Design Research Center, Carnegie-Mellon University.

a. Chose one reference from Part II of the list of potential GP applications.

b. Briefly summarize the application problem.

c. Write the mathematical model given by the author(s).

d. If possible, reformulate the model as a GP (either posynomial or signomial ) problem.

e. Identify the # of (primal) variables , # of constraints, total # of terms .

f. Describe the method used by the author(s) of the paper.

g. If sample data is given for a sample problem, or if you can guess at reasonable data, solve
the GP problem.

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