Journal
JOURNAL OF GLOBAL OPTIMIZATION
Volume 16, Issue 3, Pages 245-255Publisher
KLUWER ACADEMIC PUBL
DOI: 10.1023/A:1008308218364
Keywords
bilevel linear programming; global optimization; penalty function
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We have identified some trouble in the article 'A Penalty Function Approach for Solving Bi-Level Linear Programms' (J. Global Optimization 3: 397-419). The primal and dual compactness assumption considered is not valid. The set of cuts used in the algorithm to discard local optima is not well-defined. The test to identify possible remaining better solutions is not accurate. We redefine the cut set and correct the test. We obtain good properties for the penalized problem without assuming compactness. However, we note that the global algorithm even needs a dual compactness assumption to be well-defined. Examples are given to illustrate the remarks in the article.
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