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Dung Muu Le(ldmuumath.ac.vn) Abstract: We formulate minmax flow problems as a DC. optimization problem. We then apply a DC primaldual algorithm to solve the resulting problem.The obtained computational results show that the proposed algorithm is efficient thanks to particular structures of the minmax flow problems. Keywords: Minmax ﬂow problem · smooth DC optimization · regularization. Category 1: Global Optimization (Applications ) Category 2: Network Optimization Citation: 1. An L. T. H. and Tao P. D., The DC (Difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems, Annals of Operations Research, 133, 23  46 (2005). 2. An L. T. H., Tao P. D. and Muu L. D., Numerical solution for optimization over the efficient set by DC optimization algorithms, Operations Research Letters, 19, 117  128 (1996). 3. An L. T. H., Tao P. D. and Muu L. D., Simplicallyconstrained DC optimization over the efficient and weakly sets. J. of Optimization Theory and Applications 117, 503  531 (2003). 4. An L. T. H. and Tao P. D., Convex analysis approach to DC programming: Theory, algo rithms and applications, ACTA Mathematica Vietnamica, 22, 289  355 (1997). 5. An L. T. H. and Tao P. D., Solving a class of linearly constrained indefinite quadratic problems by DC algorithms, J.of Global Optimization, 11, 253  285 (1997). 6. Benson H. P., Optimization over the efficient set, J. Mathematical Analysis and Applica tions, 98, 56  580 (1984). 7. Benson H. P., An alllinear programming relaxation algorithm for optimization over the efficient set, J. Global Optimization, 1, 83  104 (1991). 8. Gotoh J., Thoai N. V. and Yamamoto Y., Global optimization method for solving the minimum maximal flow problem, Optimization. Methods Software, 18, 395  415 (2003). 9. Luc L. T. and Muu. L. D., A global optimization approach to optimization over the efficient set, Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, Germany, 452, 183  196 (1997). 10. Muu L .D., Computational aspects of optimization over the efficient set, Vietnam Journal of Mathematics, 23, 85  106 (1995). 11. Kim N. T. B. and Muu L.D., On the projection of the efficient set and potential applica tions, Optimization 51, 401  421 (2002). 12. Iri M., An essay in the theory of uncontrollable flows and congestion, Technical Report, Department of Information and System Engineering, Faculty of Science and Engineering, Chuo University, TRISE 94  03, (1994). 13. Iri M., Network flow  theory and applications with practical impact, in: J. Dolezal and J. Fidler (eds.) System Modelling and Optimization, Chapman and Hall, London, 24  36 (1996). 14. Philip J., Algorithms for the vector maximization problem, Mathematical Programming, 2, 207  229 (1972). 15. Quy N. V. and Muu L. D., On penalty function method for class of nonconvex constrained optimization problems, Vietnam J. of Mathematics, 29, 235  256 (2001). 16. Tao P. D., Algorithms for solving a class of non convex optimization. Methods of sub gradients, Fecmat Days 85, Mathematics for Optimization, Elservier Sience Publishers, B.V.NorthHolland (1986). 17. Shigeno M., Takahashi I. and Yamamoto Y., Minimum maximal flow problem  an opti mization over the efficient set, J. Global Optimization, 25, 425  443 (2003). 18. Shi J.M. and Yamamoto Y., A global optimization method for minimum maximal flow problem, Acta Mathematica Vietnamica, 22, 271  287 (1997). 19. Yamamoto Y. , Optimization over the efficient set: overview, J. of Global Optimization, 22, 285  317 (2002). 20. Zhu D. L. and Marcotte P., An extended descent framework for variational inequalities, J. of Optimization Theory and Applications: 80, 349  366 (1994). 21. Zenke D., Algorithms for the minimum maximal flow problem  Optimization over the efficient set, Graduate School of Systems and Information Engineering, University of Tsukuba March, (2006). Download: [PDF] Entry Submitted: 06/16/2011 Modify/Update this entry  
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