Article ID: | iaor20023009 |
Country: | Netherlands |
Volume: | 105 |
Issue: | 1 |
Start Page Number: | 213 |
End Page Number: | 226 |
Publication Date: | Jul 2001 |
Journal: | Annals of Operations Research |
Authors: | Biswal M.P., Li D., Sun X.L., Gao F. |
Keywords: | programming: convex |
We show in this paper that via certain convexification, concavification and monotonization schemes a nonconvex optimization problem over a simplex can be always converted into an equivalent better-structured nonconvex optimization problem, e.g., a concave optimization problem or a programming problem applied to the difference of two convex functions (a D.C. problem), thus facilitating the search of a global optimum by using the existing methods in concave minimization and D.C. programming. We first prove that a monotone optimization problem (with a monotone objective function and monotone constraints) can be transformed into a concave minimization problem over a convex set or a D.C. programming problem via