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**Multiobjective optimization problems with modified objective functions and cone constraints and applications.**
*(English)*
Zbl 1230.90166

Summary: 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, \((\text{MOP})_{\eta}(x)\)] and saddle points for the Lagrange function of \((\text{MOP})_{\eta}\) 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 \((\text{MOP})_{\eta}\) 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.

### MSC:

90C29 | Multi-objective and goal programming |

90C46 | Optimality conditions and duality in mathematical programming |

47J20 | Variational and other types of inequalities involving nonlinear operators (general) |

### Keywords:

multiobjective optimization problem; \(Q\)-(pseudo)invex; \(Q\)-convexlike; weakly efficient solution; saddlepoint; KKT condition; weak (strong, converse) duality; Lagrange function
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\textit{J. W. Chen} et al., J. Glob. Optim. 49, No. 1, 137--147 (2011; Zbl 1230.90166)

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