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DC programming approaches for discrete portfolio optimization under concave transaction costs

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Abstract

The paper investigates DC programming and DCA for both modeling discrete portfolio optimization under concave transaction costs as DC programs, and their solution. DC reformulations are established by using penalty techniques in DC programming. A suitable global optimization branch and bound technique is also developed where a DC relaxation technique is used for lower bounding. Numerical simulations are reported that show the efficiency of DCA and the globality of its computed solutions, compared to standard algorithms for nonconvex nonlinear integer programs.

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References

  1. Markowitz, H.M.: Portfolio selection. J. Financ. 7(1), 77–91 (1952)

    Google Scholar 

  2. Konno, H., Yamazaki, H.: Mean-absolute deviation portfolio optimization model and its application to Tokyo stock market. Manag. Sci. 37(5), 519–531 (1991)

    Article  Google Scholar 

  3. Mansini, R., Speranza, M.G.: Heuristic algorithms for portfolio selection problem with minimum transaction lots. Eur. J. Oper. Res. 114, 219–233 (1999)

    Article  MATH  Google Scholar 

  4. Kellerer, H., Mansini, R., Speranza, M.G.: Selecting portfolios with fixed costs and minimum transaction lots. Ann. Oper. Res. 99, 287–304 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bienstock, D.: Computational study of a family of mixed-integer quadratic programming problems. Math. Program. 74, 121–140 (1996)

    MathSciNet  MATH  Google Scholar 

  6. Konno, H., Wijayanayake, R.: Portfolio optimization problems under concave transaction costs and minimal transaction unit constraints. Math. Program. 89(2), 233–250 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Konno, H., Yamamoto, R.: Global optimization versus integer programming in portfolio optimization under nonconvex transaction costs. J. Glob. Optim. 32, 207–219 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Konno, H., Yamamoto, R.: Integer programming approaches in mean-risk models. Comput. Manag. Sci. 2, 339–351 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Li, D., Sun, X.L., Wang, J.: Optimal lot solution to cardinality constrained mean-variance formulation for portfolio selection. Math. Financ. 16(1), 83–101 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lin, C.C., Liu, Y.T.: Genetic algorithms for portfolio selection problems with minimum transaction lots. Eur. J. Oper. Res. 185, 393–404 (2008)

    Article  MATH  Google Scholar 

  11. Li, H.L., Tsai, J.F.: A distributed computation algorithm for solving portfolio problems with integer variables. Eur. J. Oper. Res. 186, 882–891 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hemmecke, R., Köppe, M., Lee, J., Weismantel, R.: Nonlinear Integer Programming. In: Jünger, M. et al. (eds.) 50 Years of Integer Programming 1958–2008, part 3, pp. 561–618. Springer (2010)

  13. Leyffer, S.: Deterministic methods for mixed integer nonlinear programming. Ph.D. thesis, University of Dundee, Dundee, 1993

  14. Li, D., Sun, X.L.: Nonlinear Integer Programming. Springer, New York (2006)

    MATH  Google Scholar 

  15. Le Thi, H.A., Pham Dinh, T.: A combined DC optimization—ellipsoidal branch-and-bound algorithm for solving nonconvex quadratic programming problems. J. Combin. Optim. 2(1), 9–29 (1998)

  16. Le Thi, H.A., Pham Dinh, T.: A continuous approach for large-scale constrained quadratic zero-one programming. (In honor of Professor ELSTER, Founder of the Journal Optimization) Optimization 45(3), 1–28 (2001)

  17. Le Thi, H.A., Pham Dinh, T.: A continuous approach for the concave cost supply problem via DC programming and DCA. Discret. Appl. Math. 156, 325–338 (2008)

  18. Le Thi, H.A., Pham Dinh, T.: Large-scale molecular optimization from distance matrices by a D.C. optimization approach. SIAM J. Optim. 14(1), 77–114 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  19. Le Thi, H.A., Pham Dinh, T.: The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133, 23–46 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  20. Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to DC programming: theory, algorithms and applications. Acta Mathematica Vietnamica 22(1), 289–355 (1997) [Dedicated to Professor Hoang Tuy on the occasion of his 70th birthday]

  21. Pham Dinh, T., Le Thi, H.A.: A DC optimization algorithm for solving the trust region subproblem. SIAM J. Optim. 8(2), 476–505 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  22. Hiriart-Urruty, J.B., Lemarechal, C.: Convex Analysis and Minimization Algorithms. Springer, Berlin (1993)

    Google Scholar 

  23. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)

    Book  MATH  Google Scholar 

  24. Ge, R.P., Huang, C.B.: A continuous approach to nonlinear integer programming. Appl. Math. Comput. 34, 39–60 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  25. Niu, Y.S.: Programmation DC & DCA en Optimisation Combinatoire et Optimisation Polynomiale via les Techniques de SDP. Ph.D. thesis, INSA de Rouen, France (2010)

  26. Pham, V.N.: Programmation DC et DCA pour l’optimisation non convexe/optimisation globale en variables mixtes entiè res. Codes et Applications. Ph.D. Thesis, National Institute for Applied Sciences, Rouen, April 2013

  27. Pham Dinh, T., Le Thi, H.A.: Recent advances in DC programming and DCA. Trans. Comput. Collect. Intell. 8342, 1–37 (2014)

  28. Zhang, G.: A note on “A continuous approach to nonlinear integer programming”. Appl. Math. Comput. 215, 2388–2389 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. Le Thi, H.A., Pham Dinh, T., Le, D.M.: Exact penalty in DC programming. Vietnam J. Math. 27(2), 169–178 (1999)

  30. Le Thi, H.A., Pham Dinh, T., Van Ngai, H.: Exact penalty and error bounds in DC programming. J. Glob. Optim. Special Issue in Memory of Reiner Horst, Founder of the Journal 52(3), 509–535 (2012)

  31. IBM ILOG CPLEX 12.1: ILOG optimization documentation. Software available at http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/

  32. Zangwill, W.I.: Nonlinear programming via penalty functions. Manag. Sci. 13, 344–358 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  33. Le Thi, H.A., Pham Dinh, T.: Solving a class of linearly constrained indefinite quadratic problems by DC algorithms. J. Glob. Optim. 11, 253–285 (1997)

    Article  MATH  Google Scholar 

  34. Pham Dinh, T., Nguyen Canh, N., Le Thi, H.A.: An efficient combined DCA and B&B using DC/SDP relaxation for globally solving binary quadratic programs. J. Glob. Optim. 48, 595–632 (2010)

  35. Le Thi, H.A.: An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints. Math. Program. Ser. A 87(3), 401–426 (2000)

    Article  MATH  Google Scholar 

  36. Le Thi, H.A., Van Ngai, H., Pham Dinh, T.: DC programming and DCA for general DC programs. In: Do Van, T. et al. (eds.) Advanced Computational Methods for Knowledge Engineering. Advances in Intelligent Systems and Computing, vol. 282, pp. 15–35. Springer (2014)

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Authors and Affiliations

  1. LMI, National Institute for Applied Sciences-Rouen, University of Normandie, 76801, Saint-Étienne-du-Rouvray Cedex, France

    Tao Pham Dinh, Viet Nga Pham & Yi-Shuai Niu

  2. Laboratory of Theoretical and Applied Computer Science, University of Lorraine, Ile du Saulcy, 57045, Metz, France

    Hoai An Le Thi

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  1. Tao Pham Dinh
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  2. Hoai An Le Thi
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  3. Viet Nga Pham
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  4. Yi-Shuai Niu
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Correspondence to Hoai An Le Thi.

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Pham Dinh, T., Le Thi, H.A., Pham, V.N. et al. DC programming approaches for discrete portfolio optimization under concave transaction costs. Optim Lett 10, 261–282 (2016). https://doi.org/10.1007/s11590-015-0931-2

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  • DOI: https://doi.org/10.1007/s11590-015-0931-2

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