Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON SUFFICIENT OPTIMALITY THEOREMS FOR NONSMOOTH MULTIOBJECTIVE OPTIMIZATION PROBLEMS

  • Kim, Moon-Hee (Department of Applied Mathematics Pukyong National University) ;
  • Lee, Gue-Myung (Department of Applied Mathematics Pukyong National University)
  • Published : 2001.10.01
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Abstract

We consider a nonsmooth multiobjective opimization problem(PE) involving locally Lipschitz functions and define gen-eralized invexity for locally Lipschitz functions. Using Fritz John type optimality conditions, we establish Fritz John type sufficient optimality theorems for (PE) under generalized invexity.

Keywords

References

  1. Optimization and Nonsmooth Analysis F.H. Clarke
  2. J. Inform. Optim. Sci. v.17 Various types of nonsmooth invexity G. Giorgi;A. Guerraggio
  3. J. Austal. Math. Soc. v.40 On subgradient duality with strong and weak convex functions V. Jeyakumar
  4. J. Austal. Math. Soc. Ser. v.B34 On generalized convex mathematical programming V. Jeyakumar;B. Mond
  5. J. Inform. Optim. Sci. v.12 no.2 Optimality conditions and duality theorems for multiobjective invex programs D.S. Kim;G.M. Lee
  6. Indian J. Pure Appl. Math. v.29 no.4 Nonsmooth multiobjective programs with V- p- invexity H. Kuk;G.M. Lee;D.S. Kim
  7. J. Inform. Optim. Sci. v.13 no.4 Optimality conditions in multiobjective optimization problems G.M. Lee
  8. J. Inform. Optim. Sci. v.15 no.1 Nonsmooth invexity in multiobjective programming
  9. J. Optim. Th. Appl. v.92 no.2 Optimality conditions in differentiable multiobjective programming A.A.K. Majumdar
  10. Nonlinear Programming O.L. Mangasarian
  11. J. Optim. Th. Appl. v.53 Optimality conditions in multiobjective differentiable programming C. Singh
  12. J. Math. Anal. Appl. v.206 Optimality and duality in nondifferentiable multiobjective optimization involving d-type I and related functions S.K. Suneja;M.K. Srivastava
  13. Multiobjective programming in Applications of Mathematical Programming: Theory K. Tamura;M. Iri;M. Konno(Edited by)
  14. Bull. Austral. Math. Soc. v.39 Generalized convexity and duality in multiple objective programming T. Weir;B. Mond
  15. Bull. Austral. Math. Soc. v.46 On sufficiency of the Kuhn-Tucker conditions in nondifferentiable programming F. Zhao