分形理论是非线性系统理论中最为活跃的分支之一，研究的是复杂系统产生的不光滑、不可微分的复杂几何体。
Fractal theory is the most active branch of the non-linear science, what it concerns is non-smooth and non-differential geometry produced by complex systems.
描述人造卫星运动的微分方程非常复杂，不可能给出解的解析表达式。
The differential equations that describe the artificial satellite motion are very complicated, and it is impossible to get the analytic express of solution.
接着，利用函数的上次微分构造了不可微向量优化问题（VP）的广义对偶模型，并且在适当的弱凸性条件下建立了弱对偶定理。
Finally, the generalized dual model of the problem (VP) is presented with the help of upper subdifferential of function, and a weak duality theorem is given.
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