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On DC. optimization algorithms for solving minmax flow problems

Dung Muu Le(ldmuu***at***math.ac.vn)
Quang Thuy Le(thuylq-fami***at***mail.hut.edu.vn)

Abstract: We formulate minmax flow problems as a DC. optimization problem. We then apply a DC primal-dual 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., Simplically-constrained 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 all-linear 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).

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Entry Submitted: 06/16/2011
Entry Accepted: 06/18/2011
Entry Last Modified: 06/16/2011

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