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 s et of cuts used in the algorithm to discard local optima is not well-define d. The test to identify possible remaining better solutions is not accurate . We redefine the cut set and correct the test. We obtain good properties f or the penalized problem without assuming compactness. However, we note tha t the global algorithm even needs a dual compactness assumption to be well- defined. Examples are given to illustrate the remarks in the article.