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Mathematics for Interval Algebra and Optimization

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Power System Operation with Large Scale Stochastic Wind Power Integration

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

This chapter introduces some mathematical algorithms for solving interval linear equations, interval nonlinear equations, interval nonlinear equations and interval robust optimization models.

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References

  1. Guessous N, Souhar O (2004) Recursive two-level ILU preconditioner for nonsymmetric M-matrices. J Appl Math Comput 16(1–2):19–35

    Article  MathSciNet  MATH  Google Scholar 

  2. Cui X, Hayami K (2009) Generalized approximate inverse preconditioners for least squares problems. Jpn J Ind Appl Math 26(1):1–14

    Article  MathSciNet  MATH  Google Scholar 

  3. Griffel DH (2002) Applied functional analysis. G. P. C. Press, Canada

    MATH  Google Scholar 

  4. Al-Khayyal FA, Larsen C, Van Voorhis T (1995) A relaxation method for nonconvex quadratically constrained quadratic programs. J Global Optim 6(3):215–230

    Article  MathSciNet  MATH  Google Scholar 

  5. Androulakis IP, Maranas CD, Floudas CA (1995) αBB: a global optimization method for general constrained nonconvex problems. J Global Optim 7(4):337–363

    Article  MathSciNet  MATH  Google Scholar 

  6. Maranas CD, Floudas CA (1995) Finding all solutions of nonlinearly constrained systems of equations. J Global Optim 7(2):143–182

    Article  MathSciNet  MATH  Google Scholar 

  7. Raber U (1998) A simplicial branch-and-bound method for solving nonconvex all-quadratic programs. J Global Optim 13(4):417–432

    Article  MathSciNet  MATH  Google Scholar 

  8. Linderoth J (2005) A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs. Math Program 103(2):251–282

    Article  MathSciNet  MATH  Google Scholar 

  9. Floudas CA, Pardalos PM, Nahapetyan AG (2009) Bilinear programming. In: Floudas CA, Pardalos PM (eds) Encyclopedia of optimization. Springer, US, pp 279–282

    Google Scholar 

  10. Shapiro JF (1984) A note on node aggregation and Benders’ decomposition. Math Program 29(1):113–119

    Article  MathSciNet  MATH  Google Scholar 

  11. Henry J, Yvon J, Lahdelma R et al (1994) A modified benders’ decomposition technique for solving large scale unit commitment problems. In: Henry J, Yvon J (eds) System modelling and optimization. Springer, Berlin, pp 737–745

    Google Scholar 

  12. Floudas CA, Pardalos PM, Floudas CA (2001) Generalized benders decomposition. In: Floudas CA, Pardalos PM (eds) Encyclopedia of optimization. Springer, US, pp 747–758

    Google Scholar 

  13. Gass SI, Fu MC (2013) Benders decomposition method. In: Gass SI, Fu MC (eds) Encyclopedia of operations research and management science. Springer, US, p 115

    Google Scholar 

  14. Zeng B, Zhao L (2013) Solving two-stage robust optimization problems using a column-and-constraint generation method. Oper Res Lett 41(5):457–461

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Xi’an Jiaotong University, Xi’an, China

    Tao Ding

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  1. Tao Ding
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Correspondence to Tao Ding .

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© 2017 Springer Science+Business Media Singapore

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Ding, T. (2017). Mathematics for Interval Algebra and Optimization. In: Power System Operation with Large Scale Stochastic Wind Power Integration. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-2561-7_2

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  • DOI: https://doi.org/10.1007/978-981-10-2561-7_2

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-2560-0

  • Online ISBN: 978-981-10-2561-7

  • eBook Packages: EnergyEnergy (R0)

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