...nonlinear semidefinite programming, augmented Lagrangian, spectral penalty, implicit function theorem. 1. Introduc[gap=134]关键词：矩阵不等式，非线性半定规划，增广拉格朗日，光谱罚款，隐函数存在定理。 1。
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并给出了非线性半定规划的最优性必要和充分条件。
Finally, optimality necessary and sufficient conditions for nonlinear convex semidefinite programming are proved.
第五章，给出了解凸非线性半定规划的一种广义拉格朗日算法。
In the fifth chapter, we introduce an Augmented Lagrangian method for solving convex Nonlinear Semidefinite Programming (NLSDP) problems.
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