Multiple Objective Programming Involving Differentiable (Hp, r)-invex Functions

• Xiaoling Liu ^[1] ; Dehui Yuan ^[1] ; Shengyun Yang ^[1] ; Guoming Lai ^[1] ; Chuanqing Xu ^[2]
  1. [1] Hanshan Normal University

     Hanshan Normal University

     China

     
  2. [2] Beijing Armed Forced Eng. Institute Department of Mathematics
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 13, Nº. 1, 2011, págs. 125-136
• Idioma: inglés
• DOI: 10.4067/S0719-06462011000100008
• Enlaces
  • Texto completo
• Resumen
  • español

    Este trabajo, establece nuevos tipos de funciones convexas generalizadas que incluyen localmente funciones (Hp, r) de pre-invex y funciones (Hp, r)-invex. La relacin entre estas dos nuevas clases de funciones estn establecidas. Tambin se presentan las condiciones de optimalidad en diferenciables problemas de programacin matemtica, donde las funciones consideradas en este artculo son funciones (Hp, r)-invex.

  • English

    In this paper, we introduce new types of generalized convex functions which include locally (Hp, r)-pre-invex functions and (Hp, r)-invex functions. Relationship between these two new classes of functions are established. We also present the conditions for optimality in differentiable mathematical programming problems where the functions considered are (Hp, r)-invex functions introduced in this paper.

• Referencias bibliográficas
  • Antczak, T. (2002). Lipschitz r-Invex Functions and Nonsmooth Programming. Numerical Functional Analysis and Optimization. 23. 265-283
  • Antczak, T. (2003). Generalized (p, r)-Invexity in Mathematical Programming. Numerical Functional Analysis and Optimization. 24. 437-453
  • Antczak, T. (2001). p, r)-Invex Sets and Functions. Journal of Mathematical Analysis and Applications. 263. 355-379
  • Antczak, T. (2001). On (p, r)-Invexity-Type Nonlinear Programming Problems. Journal of Mathematical Analysis and Applications. 264. 382-397
  • Avriel, M. (1976). Nonlinear Programming: Analysis and Methods. Prentice-Hall,Englewood cliffs. New Jersey.
  • Avriel, M,Zang, I. (1980). Generalized arcwise-connected functions and characterization of local-global minimum properties. Journal of Optimization...
  • Ben-Israel, A,Mond, B. (1986). What is Invexity?. Journal of the Australian Mathematical Society, Series B. 28. 1-9
  • Clarke, F.H. (1983). Optimization and Nonsmooth Analysis. Jone Wiley and Sons. New York.
  • Cromme, L. (1978). Strong Uniqueness: A Far-Reaching Criterion for the Convergence of Iterative Procedures. Numer.Math. 29. 179-193
  • Ewing, G.M. (1977). Sufficient Conditions for Global Minima of Suitable Convex Functions from Variational and Control Theory. SIAM review....
  • Hanson, M.A. (1981). On Sufficiency of the Kuhn-Tucker Conditions. Journal of Mathematical Analysis and Applications. 80. 545-550
  • Hanson, M.A,Mond, B. (1987). Necessary and Sufficient Conditions in Constrained Optimization. Math. Programming. 37. 51-58
  • Kaul, R.N,Kaur, S. (1985). Optimality Criteria in Nonlinear Programming Involving Nonconvex Functions. Journal of Mathematical Analysis and...
  • Kaul, R.N,Lyall, V,Kaur, S. (1988). Locally Connected Sets and Functions. Journal of Mathematical Analysis and Applications. 134. 30-45
  • Kaul, R.N,Lyall, V. (1991). Locally Connected Functions and Optimality. Indian Journal of Pure Applied Mathematics. 22. 99-108
  • Klatte, D. (1995). Stable Local Minimizers in Semi-Infinite Optimization: Regularity and SecondOrder Conditions. Journal of Computational...
  • Liu, S.Y. (1989). Optimality Conditions for Nonsmooth Multiobjective Programming. Journal of Systems Science and Mathematical Science. 19....
  • Lyall, V,Suneja, S.K,Aggarwal, S. (1997). Fritz-John Optimality and Duality for NonConvex Programs. Journal of Mathematical Analysis and Applications....
  • Mishra, S.K,Wang, S.Y,Lai, K.K. (2004). Complex Minimax Programming under Generalized Convexity. Journal of Computational and Applied Mathematics....
  • Mohan, S.R,Neogy, S.K. (1995). On Invex Sets and Preinvex Functions. Journal of Mathematical Analysis and Applications. 189. 901-908
  • Pini, R. (1991). Invexity and Generalized Convexity. Optimization. 22. 513-525
  • Rokafellar, R.T. (1970). Convex Analysis. Princton Press. New Jersey.
  • Sun, M.B,Yang, X.P. (2004). Inequalities of Hadamard Type for r-Convex Functions in Carnot Groups. Acta Mathematicae Applicatae Sinica. 20....
  • Suneja, S.K,Srivastava, M.K. (1997). Optimality and Duality in Nondifferentiable Multiobjective Optimization Involving d-Type I and Related...
  • Weir, T,Mond, B. (1988). Preinvex Functions in Multiple-Objective Optimization. Journal of Mathematical Analysis and Applications. 136. 29-38
  • Weir, T,Jeyakumar, V. (1988). A Class of Nonconvex Functions and Mathematical Programming. Bulletin of the Australian Mathematical Society....
  • Chinchuluun, A,Yuan, D.H,Pardalos, P.M. (2007). Optimality Conditions and Duality for Nondifferentiable Multiobjective Fractional Programming...
  • Yuan, D.H,Liu, X.L,Chinchuluun, A,Pardalos, P.M. (2006). Nondifferentiable Minimax Fractional Programming Problems. Journal of Optimization...
  • Yuan, D.H,Liu, X.L,Yang, S.Y,Nyamsuren, D,Altannar, C. (2007). Optimality Conditions and Duality for Nonlinear Programming Problems Involving...