The Geometry of Cone-lp's
The Geometry of Cone-lp's
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Cone-lp 的几何形状
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通讯作者：
G. Abor Pataki
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作者：
G. Abor Pataki
给出了凸规划的圆锥曲线公式，我们描述了一个刻画可行集的面的理论。Deenes的非退化性，严格互补性，并将这些与最佳的脸，类似于LP的情况下。刻画可行集的切空间。介绍了与上述集合的维数有关的边界结构不等式族。使用的一般框架，给出了一个简单的推导一些结构的结果，可以制定为SDP的问题。展示了如何处理两个算法方面：将一个可行的解决方案转换为一个，这也是一个极端点;并执行限制敏感性分析。
Given the conic formulation of a convex program, we describe a theory that Characterizes the faces of the feasible sets. Deenes nondegeneracy, strict complementarity and relates these to the optimal face, analogously to the LP case. Characterizes the tangent spaces of the feasible sets. Introduces the family of boundary structure inequalities which relate the dimensions of the above-mentioned sets. Using the general framework, gives a simple derivation for a number of structural results about problems that can be formulated as an SDP. Shows how two algorithmic aspects can be handled: converting a feasible solution into one, which is also an extreme point; and performing a restricted sensitivity analysis.