在本文中,我们考虑约束函数带有不确定信息的凸半无限优化问题的近似解(也称为ε-解),并建立了凸半无限规划的鲁棒对等问题,同时给出了其近似解.进一步地,提出了鲁棒对偶问题的必要条件和充分条件.在锥约束条件下,基于鲁棒优化方法,证明了近似解意义下的拉格朗日对偶性质.
In this paper,we consider the approximate solutions(also called e-solutions)for semi-infinite optimization problems that objective function and constraint functions with uncertain data are all convex,then the robust counterpart of convex semi-infinite program is established and the approximate solutions are considered.Moreover,the robust necessary condition and robust sufficient theorems are obtained.Additional,the Lagrangian duality results in the sense of the approximate solution are given by the robust optimization approach under the proposed cone constraint qualification.