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Bilevel Programming Problems


A mathematical programming problem is classified as a Bilevel Programming Problem when one of the constraints of an optimization problem is also an optimization problem. Bilevel problems occur in diverse applications, such as economics, civil engineering, and chemical engineering.

Section 1: Karush-Kuhn-Tucker Approach

Test Problem

Description

AMPL Model File

AMPL Data File

1

Clark-Westerberg (1990a)

ex9.1.1.mod

ex9.1.1.dat

2

Liu-Hart (1994)

ex9.1.2.mod

ex9.1.2.dat

3

Candler-Townsley (1982)

ex9.1.3.mod

ex9.1.3.dat

4

Clark-Westerberg (1988)

ex9.1.4.mod

ex9.1.4.dat

5

Bard (1991)

ex9.1.5.mod

ex9.1.5.dat

6

Anandalingam-White (1990)

ex9.1.6.mod

ex9.1.6.dat

7

Bard-Falk (1982)-I

ex9.1.7.mod

ex9.1.7.dat

8

Bard-Falk (1982)-II

ex9.1.8.mod

ex9.1.8.dat

9

Visweswaran-et.al., (1996)

ex9.1.9.mod

ex9.1.9.dat

10

Tuy-et.al., (1993)

ex9.1.10.mod

ex9.1.10.dat

Section 2: Bilevel Quadratic Programming Problems

Test Problem

Description

AMPL Model File

AMPL Data File

1

Convex quadratic-quadratic BLPP

ex9.2.1.mod

ex9.2.1.dat

2

Shimizu-Aiyoshi (1981)

ex9.2.2.mod

ex9.2.2.dat

3

Visweswaran-et.al., (1996)-I

ex9.2.3.mod

ex9.2.3.dat

4

Yezza (1996)-I

ex9.2.4.mod

ex9.2.4.dat

5

Clark-Westerberg (1990a)

ex9.2.5.mod

ex9.2.5.dat

6

Falk-Liu (1995)

ex9.2.6.mod

ex9.2.6.dat

7

Visweswaran-et.al., (1996)-II

ex9.2.7.mod

ex9.2.7.dat

8

Yezza (1996)-II

ex9.2.8.mod

ex9.2.8.dat

9

Bard (1991)

ex9.2.9.mod

ex9.2.9.dat

 

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