Name
Abstract | ||
|---|---|---|
The multi-level programming problem is defined as an n -person nonzero-sum game with perfect information in which the players move sequentially. The bi-level linear case is addressed in detail. Solutions are obtained by recasting this problem as a standard mathematical probram and appealing to its implicitly separable structure. The reformulated optimization problem is linear save for a complementarity constraint of the form 〈 u , g 〉 = 0. This constraint is decomposed in a manner that permits us to achieve separability with very little cost in dimensionality. A general branch and bound algorithm is then applied to obtain solutions. Unlike the conventional mathematical program though, the multi-level program may fail to have a solution even when the decision variables are defined over a compact set. An auxiliary optimization problem is employed to detect such failure. Finally, the general max-min problem is discussed within the bi-level programming framework. Examples are given for a variety of related problems. |
Year | DOI | Venue |
|---|---|---|
1982 | 10.1016/0305-0548(82)90007-7 | COMPUTERS & OPERATIONS RESEARCH |
DocType | Volume | Issue |
Journal | 9 | 1 |
ISSN | Citations | PageRank |
0305-0548 | 166 | 30.28 |
References | Authors | |
6 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jonathan F. Bard | 1 | 1428 | 144.29 |
| James E. Falk | 2 | 297 | 68.47 |