自反Banach空间中锥线性优化问题强对偶成立的一个充分条件

A SUFFICIENT CONDITION FOR DUALITY OF CONIC LINEAR OPTIMIZATIONS IN REFLEXIVE BANACH SPACES

讨论自反Banach空间中锥线性优化问题的强对偶成立的一个充分条件.在自反Banach空间中,当原问题的最优值是有限的且约束集C的对偶锥的内部非空时,若存在某个原问题目标函数的水平集是有界的,则强对偶成立.

We prove that when the optimal value of the primal optimization is finite and int C ° ≠Ф, if it exists a level set of the primal optimization is bounded, then the strong duality holds, in reflexive Banach spaces.