非线性半定规划的雅可比唯一性定理

摘要

Jacobian uniqueness conditions for nonlinear semidefinite programming are presented, under which,the mapping characterizing the KKT conditions is demonstrated to have a nonsingular derivative at the KKT point. Under the Jacobian uniqueness conditions, stability theorem for nonlinear semidefinite programming is proved and the necessary optimality conditions for a special bi-level program,whose lower level problem is a nonlinear semidefinite optimization problem,are established.%提出了非线性半定规划的雅可比唯一性条件，证明在这一条件下，刻画 KKT 条件的映射在KKT点处导数是非奇异的。在雅可比唯一性条件下，证明了非线性半定规划的稳定性定理并建立了下层为非线性半定优化问题的一类特殊双层规划的必要性最优条件。