A note on a penalty function approach for solving bilevel linear programs

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.