This paper mainly focuses on optimality conditions for efficient solutions of a nonconvex constrained multiobjective optimization problem via image space analysis. By virtue of the Gerstewitz function and the sum of the components of the objective function, a nonlinear regular weak separation function for efficient solutions, is constructed. In order to illustrate the importance of the sum of the components of the objective function in the nonlinear regular weak separation function for efficient solutions, a nonlinear regular weak separation function for weak efficient solutions, is also given. Moreover, a nonlinear strong separation function for efficient and weak efficient solutions, is introduced. Then, some theorems of the weak and strong alternative and a global necessary and sufficient optimality condition for efficient solutions are derived by means of the nonlinear regular weak and strong separation functions for efficient solutions. A saddle point sufficient optimality condition for efficient solutions in terms of a generalized Lagrangian function associated with the nonlinear regular weak separation function, is established. Finally, under some suitable assumptions, a saddle point necessary optimality condition is obtained, which further yields a Karush/Kuhn–Tucker necessary optimality condition for efficient solutions by the Clarke subdifferential.

本文主要关注通过图像空间分析有效解决非凸约束多目标优化问题的最优条件。凭借 Gerstewitz 函数和目标函数的分量之和，构造了用于有效解的非线性正则弱分离函数。为了说明非线性正则弱分离函数中目标函数分量之和对于有效解的重要性，还给出了弱有效解的非线性正则弱分离函数。此外，还介绍了用于有效和弱有效解决方案的非线性强分离函数。然后，通过有效解的非线性正则弱强分离函数，推导出了一些弱强替代定理和有效解的全局充分必要最优条件。根据与非线性正则弱分离函数相关的广义拉格朗日函数，建立了有效解的鞍点充分最优条件。最后，在一些合适的假设下，获得了鞍点必要最优条件，这进一步产生了克拉克次微分有效解的 Karush/Kuhn-Tucker 必要最优条件。根据与非线性正则弱分离函数相关的广义拉格朗日函数，建立了有效解的鞍点充分最优条件。最后，在一些合适的假设下，获得了鞍点必要最优条件，这进一步产生了克拉克次微分有效解的 Karush/Kuhn-Tucker 必要最优条件。根据与非线性正则弱分离函数相关的广义拉格朗日函数，建立了有效解的鞍点充分最优条件。最后，在一些合适的假设下，获得了鞍点必要最优条件，这进一步产生了克拉克次微分有效解的 Karush/Kuhn-Tucker 必要最优条件。