# 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

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

**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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