THE CENTRAL PATH IN SMOOTH CONVEX SEMIDEFINITE PROGRAMS
THE CENTRAL PATH IN SMOOTH CONVEX SEMIDEFINITE PROGRAMS
复制标题
光滑凸半定规划的中心路径
DOI：
10.1080/02331930290019396
复制
发表时间：
2002
期刊：
影响因子：
2.2
通讯作者：
Y. Peterzil
中科院分区：
文献类型：
--
作者：
L. M. G. Drummond;Y. Peterzil
摘要本文研究了具有光滑目标函数和约束函数的非线性凸半定规划问题中心路的良定性。在标准假设下，我们证明了中心路的存在性等价于最优集的非空性和有界性。给出了其它等价条件，如存在严格对偶可行点或存在单个中心点。还讨论了原始和对偶对数障碍以及原始和对偶目标函数沿着轨迹的单调行为。最后，在数据函数解析性的附加假设下，证明了原始-对偶轨道的收敛性。
Abstract In this paper we study the welldefinedness of the central path associated to a nonlinear convex semidefinite programming problem with smooth objective and constraint functions. Under standard assumptions, we prove that the existence of the central path is equivalent to the nonemptiness and boundedness of the optimal set. Other equivalent conditions are given, such as the existence of a strictly dual feasible point or the existence of a single central point. The monotonic behavior of the primal and dual logarithmic barriers and of the primal and dual objective functions along the trajectory is also discussed. The existence and optimality of cluster points is established and finally, under the additional assumption of analyticity of the data functions, the convergence of the primal-dual trajectory is proved.