Multiobjective optimization problems with modified objective functions and cone constraints and applications

  • Authors:

  • Jia Wei Chen;Yeol Je Cho;Jong Kyu Kim;Jun Li

  • Affiliations:

  • School of Mathematics and Information, China West Normal University, Nanchong, Pepole's Republic of China 637002;Department of Mathematics Education and The RINS, College of Education, Gyeongsang National University, Chinju, Korea 660-701;Department of Mathematics, Kyungnam University, Masan, Korea 631-701;School of Mathematics and Information, China West Normal University, Nanchong, Pepole's Republic of China 637002

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2011

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Abstract

In this paper, we consider a differentiable multiobjective optimization problem with generalized cone constraints (for short, MOP). We investigate the relationship between weakly efficient solutions for (MOP) and for the multiobjective optimization problem with the modified objective function and cone constraints [for short, (MOP) 驴 (x)] and saddle points for the Lagrange function of (MOP) 驴 (x) involving cone invex functions under some suitable assumptions. We also prove the existence of weakly efficient solutions for (MOP) and saddle points for Lagrange function of (MOP) 驴 (x) by using the Karush-Kuhn-Tucker type optimality conditions under generalized convexity functions. As an application, we investigate a multiobjective fractional programming problem by using the modified objective function method.