Journal of Optimization Theory and Applications

, Volume 112, Issue 1, pp 145–165 | Cite as

Composite Nonsmooth Optimization Using Approximate Generalized Gradient Vectors

  • M. S. Kim
  • D. H. Choi
  • Y. Hwang
Article

Abstract

A new approximation method is presented for directly minimizing a composite nonsmooth function that is locally Lipschitzian. This method approximates only the generalized gradient vector, enabling us to use directly well-developed smooth optimization algorithms for solving composite nonsmooth optimization problems. This generalized gradient vector is approximated on each design variable coordinate by using only the active components of the subgradient vectors; then, its usability is validated numerically by the Pareto optimum concept. In order to show the performance of the proposed method, we solve four academic composite nonsmooth optimization problems and two dynamic response optimization problems with multicriteria. Specifically, the optimization results of the two dynamic response optimization problems are compared with those obtained by three typical multicriteria optimization strategies such as the weighting method, distance method, and min–max method, which introduces an artificial design variable in order to replace the max-value cost function with additional inequality constraints. The comparisons show that the proposed approximation method gives more accurate and efficient results than the other methods.

Composite nonsmooth optimization approximation generalized gradient vector 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • M. S. Kim
    • 1
  • D. H. Choi
    • 2
  • Y. Hwang
    • 3
  1. 1.Center of Innovative Design Optimization Technology(iDOT)Hanyang UniversitySeoulKorea
  2. 2.Center of Innovative Design Optimization Technology(iDOT)Hanyang UniversitySeoulKorea
  3. 3.Department of Mathematical EducationKonkuk UniversitySeoulKorea

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