Skip to main content

Advertisement

SpringerLink
Log in

Application of Stochastic Programming Technique to Solve Interval Quadratic Programming Problem

  • Original Paper
  • Published:
International Journal of Applied and Computational Mathematics Aims and scope Submit manuscript

Abstract

In this paper we developed a methodology to solve interval quadratic programming problem (IQPP). In the proposed work we convert interval quadratic programming problem (IQPP) into a non-interval stochastic programming problem. We transform the interval valued objective function into function of random variables and corresponding equality/inequality interval valued constraints into stochastic constraints using Gaussian distribution and 6σ-rule. Using this transformation method we tried to develop a solution of native interval quadratic programming problem. The methodologies are illustrated with numerical examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Beasley, J.E.: Heuristic Algorithms for the Unconstrained Binary Quadratic Programming Problem. London, England (1998)

  2. Caballero, R., Cerda, E., Munoz, M., Rey, L., Stancu-Minasian, I.: Efficient solution concepts and their relations in stochastic multiobjective programming. J. Optim. Theory Appl. 110(1), 53–74 (2001)

    Article  MathSciNet  Google Scholar 

  3. Chalco-Cano, Y., Román-Flores, H., Jiménez-Gamero, M.D.: Generalized derivative and π-derivative for set-valued functions. Inf. Sci. 181, 2177–2188 (2011)

    Article  MathSciNet  Google Scholar 

  4. Hladik, M.: Interval convex quadratic programming problems in a general form. CEJOR 25(3), 725–737 (2017)

    Article  MathSciNet  Google Scholar 

  5. Hormazdabadi, M.G., Nehi, H.M., Allahdadi, M.: Optimal solution set in interval quadratic programming problem. J. Math. Ext. 14(2), 189–205 (2020)

    Google Scholar 

  6. Hukuhara, P.M.: Integration des Applicaitons Mesurables dont la Valeurest un Compact Convexe. Funkcialaj Ekvacioj 10(3), 205–223 (1967)

    MathSciNet  MATH  Google Scholar 

  7. Jiang, C., Han, X., Liu, G.R.: A nonlinear interval number programming method for uncertain optimization problems. Eur. J. Oper. Res. 188, 1–13 (2008)

    Article  MathSciNet  Google Scholar 

  8. Kumar, P., Panda, G.: Solving nonlinear interval optimization problem using stochastic programming technique. Opsearch 54(4), 752–765 (2017)

    Article  MathSciNet  Google Scholar 

  9. Liu, S.T., Wang, R.T.: A numerical solution method to interval quadratic programming. Appl. Math. Comput. 189(2), 1274–1281 (2007)

    MathSciNet  MATH  Google Scholar 

  10. Li, W., Tian, X.: Numerical solution method for general interval quadratic programming. Appl. Math. Comput. 202, 589–595 (2008)

    MathSciNet  MATH  Google Scholar 

  11. Li, W., Xia, M., Li, H.: Some results on the upper bound of optimal values in interval convex quadratic programming. J. Comput. Appl. Math. 302, 38–49 (2016)

    Article  MathSciNet  Google Scholar 

  12. Lodwick, W.A.: Constrained Interval Arithmetic. Citeseer (1999)

  13. Markov, S.: Calculus for interval functions of a real variable. Computing 22, 325–337 (1979)

    Article  MathSciNet  Google Scholar 

  14. Moore, R.E.: Interval Analysis. Prentice-Hall, Englewood Cliffs (1966)

    MATH  Google Scholar 

  15. Moore, R.E.: Methods and Applications of Interval Analysis. SIAM, Philadelphia (1979)

    Book  Google Scholar 

  16. Ouail, F.Z., Chergui, M.E.A.: A branch-and-cut technique to solve multiobjective integer quadratic programming problems. Ann. Oper. Res. 267(1–2), 431–446 (2018)

    Article  MathSciNet  Google Scholar 

  17. Taghi-Nezhad, N., Taleshian, F., Shahini, M.: A new approach for solving interval quadratic programming problem. Iran. J. Optim. 11(1), 67–75 (2019)

    Google Scholar 

  18. Stancu-Minasian, I., Wets, M.: A research bibliography in stochastic programming. Oper. Res. 24(6), 1078–1119 (1976)

    Article  MathSciNet  Google Scholar 

  19. Stancu-Minasian, I.M.: Stochastic Programming with Multiple Objective Functions, vol. 13. D Reidel Pub Co, Dordrecht (1984)

    MATH  Google Scholar 

  20. Stefanini, L., Bede, B.: Generalized Hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Anal. 71, 1311–1328 (2009)

    Article  MathSciNet  Google Scholar 

  21. Syaripuddin, Suprajithno, H., Fatmavati, F.: Solution of quadratic programming with interval variables using a two-level programming approach. J. Appl. Math. 2018(5), 1–7 (2018)

    Article  MathSciNet  Google Scholar 

  22. Vanaret, C.: Hybridization of interval methods and evolutionary algorithm for solving difficult optimization problems (2020). arXiv preprint arXiv:2001.11465

  23. Zhou, J., Cheng, S., Li, M.: Sequential quadratic programming for robust optimization with interval uncertainty. J. Mech. Des. 134(10), 100913-100913-13 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Solan, H.P., 173234, India

    Shaveta Kumari & Saurabh Srivastava

Authors
  1. Shaveta Kumari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saurabh Srivastava
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saurabh Srivastava.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kumari, S., Srivastava, S. Application of Stochastic Programming Technique to Solve Interval Quadratic Programming Problem. Int. J. Appl. Comput. Math 7, 17 (2021). https://doi.org/10.1007/s40819-020-00947-7

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40819-020-00947-7

Keywords

Mathematics Subject Classification

Search

Navigation