【Key words】 multiobjective control problem； efficiency solutions； mixed type duality； generalized V-invexity.；
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引入对偶变量，进一步建立使问题化为在以混合变量组成的全状态辛空间中的控制正则方程和初边条件。
By introducing dual variables, the dual governing equations and boundary conditions, which are composed by mixed variables under whole state space, are obtained.
考虑到混合边界值条件下，对偶积分方程的刚性扭转振动建立了横观各向同性饱和地基上圆板的休息。
Considering the mixed boundary-value conditions, the dual integral equations of torsional vibrations of a rigid circular plate resting on transversely isotropic saturated soil were established.
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