Genericity Results in Linear Conic Programming - A Tour d'Horizon
Genericity Results in Linear Conic Programming - A Tour d'Horizon
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DOI：
10.1287/moor.2016.0793
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发表时间：
2017-02
期刊：
影响因子：
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通讯作者：
Mirjam Dür;Bolor Jargalsaikhan;G. Still
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文献类型：
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作者：
Mirjam Dür;Bolor Jargalsaikhan;G. Still
本文研究一般线性锥规划的一般性质。在过去的二十年里，在这个问题上已经取得了许多成果。例如，它是已知的唯一性，严格互补性，和非退化的最佳解决方案持有几乎所有的问题的情况。强对偶性一般在更强的意义上成立，即，它适用于问题实例的一般子集。在本文中，我们调查已知的结果，并提出新的。特别地，我们给出了一个简单的证明的事实，斯莱特的条件持有一般的线性锥规划。我们进一步讨论了唯一性、非退化性和严格互补性的稳定性问题。我们还评论的事实是，在一般情况下，一个圆锥形的程序不能被视为一个光滑的问题，需要从非光滑几何测度理论的技术。
This paper is concerned with so-called generic properties of general linear conic programs. Many results have been obtained on this subject during the last two decades. For example, it is known that uniqueness, strict complementarity, and nondegeneracy of optimal solutions hold for almost all problem instances. Strong duality holds generically in a stronger sense, i.e., it holds for a generic subset of problem instances. In this paper, we survey known results and present new ones. In particular we give an easy proof of the fact that Slater’s condition holds generically in linear conic programming. We further discuss the problem of stability of uniqueness, nondegeneracy, and strict complementarity. We also comment on the fact that in general, a conic program cannot be treated as a smooth problem and that techniques from nonsmooth geometric measure theory are needed.