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Solving Hemivariational Inequalities by Nonsmooth Optimization Methods

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Encyclopedia of Optimization

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Keywords

Discrete Problem

Numerical Realization

Nonsmooth Optimization Methods

Numerical Experience

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References

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References

  1. Bonnans JF, Gilbert JC, Lemarèchal C, Sagastizàbal C (1995) A family of variable metric proximal methods. Math Program 68:15–47

    Google Scholar 

  2. Ciarlet PG (1978) The finite element method for elliptic problems. North-Holland, Amsterdam

    Book  MATH  Google Scholar 

  3. Clarke FH (1983) Optimization and nonsmooth analysis. Wiley, New York

    MATH  Google Scholar 

  4. Kelley JE (1960) The cutting plane method for solving convex programs. SIAM J 8:703–712

    MathSciNet  Google Scholar 

  5. Kiwiel KC (1985) Methods of descent for nondifferentiable optimization. Springer, Berlin

    MATH  Google Scholar 

  6. Kiwiel KC (1990) Proximity control in bundle methods for convex nondifferentiable optimization. Math Program 46:105–122

    Article  MathSciNet  MATH  Google Scholar 

  7. Lemarèchal C, Strodiot J-J, Bihain A (1981) On a bundle algorithm for nonsmooth optimization. In: Mangasarian OL, Mayer RR, Robinson SM (eds) Nonlinear Programming. Acad. Press, New York, pp 245–281

    Google Scholar 

  8. Lukšan L, Vlček J (1995) A bundle-Newton method for nonsmooth unconstrained minimization. Techn. Report Inst. Computer Sci. Acad. Sci. Czech Republic 654

    Google Scholar 

  9. Miettinen M, Haslinger J (1995) Approximation of nonmonotone multivalued differential inclusions. IMA J Numer Anal 15:475–503

    Article  MathSciNet  MATH  Google Scholar 

  10. Miettinen M, Haslinger J (1997) Finite element approximation of vector-valued hemivariational inequalities. J Global Optim 10:17–35

    Article  MathSciNet  MATH  Google Scholar 

  11. Miettinen M, Mäkelä MM, Haslinger J (1995) On numerical solution of hemivariational inequalities by nonsmooth optimization methods. J Global Optim 6:401–425

    Article  MathSciNet  MATH  Google Scholar 

  12. Mäkelä MM, Miettinen M, Lukšan L, Vlček J (1999) Comparing nonsmooth nonconvex bundle methods in solving hemivariational inequalities. J Global Optim 14:117–135

    Article  MathSciNet  MATH  Google Scholar 

  13. Mäkelä MM, Neittaanmäki P (1992) Nonsmooth optimization: Analysis and algorithms with applications to optimal control. World Sci., Singapore

    MATH  Google Scholar 

  14. Naniewicz Z, Panagiotopoulos PD (1995) Mathematical theory of hemivariational inequalities and applications. M. Dekker, New York

    Google Scholar 

  15. Panagiotopoulos PD (1993) Hemivariational inequalities. Applications in mechanics and engineering. Springer, Berlin

    MATH  Google Scholar 

  16. Schramm H, Zowe J (1992) A version of the bundle idea for minimizing a nonsmooth functions: Conceptual idea, convergence analysis, numerical results. SIAM J Optim 2:121–152

    Article  MathSciNet  MATH  Google Scholar 

  17. Shor NZ (1985) Minimization methods for non‐differentiable functions. Springer, Berlin

    MATH  Google Scholar 

  18. Wolfe P (1975) A method of conjugate subgradients for minimizing nondifferentiable functions. Math Program Stud 3:145–173

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. University Jyväskylä, Jyväskylä, Finland

    Markku Miettinen & Marko M. Mäkelä

Authors
  1. Markku Miettinen
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  2. Marko M. Mäkelä
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

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© 2008 Springer-Verlag

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Miettinen, M., Mäkelä, M.M. (2008). Solving Hemivariational Inequalities by Nonsmooth Optimization Methods . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_626

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