论文标题
线性半明确可行性问题上的内点算法的超线性收敛性
Superlinear Convergence of an Interior Point Algorithm on Linear Semi-definite Feasibility Problems
论文作者
论文摘要
在文献中，除了假设严格的互补性外，使用已知的搜索方向，可实施多项式时间内部点算法的超线性收敛，即HKM方向，双重或NT方向求解半决赛（SDP）（SDPS）由（i）表明（i），假设给定的nodifation nodific and nifific and nifific andific andific sidific sitific sitific sitific sifific sitific sifific sitific sifific sitifie sitifific sitifific sitifific sifific sitifific sitifific siths [ （ii）考虑特殊类别的SDP，例如线性半明确可行性问题（LSDFPS），并要求初始迭代到算法以满足某些条件[26，27]。否则，即使这些算法证明具有多项式迭代复杂性和超线性收敛，这些算法也不容易实现[14]。 [26，27]中的条件是，在求解LSDFP时，必须满足算法的初始迭代才能满足超线性收敛性。在本文中，我们提出了一种实用的初始迭代，以实现可实现的内部点算法，该算法可以保证当使用算法来求解LSDFP的均匀可行性模型时，可以保证超线性收敛。
In the literature, besides the assumption of strict complementarity, superlinear convergence of implementable polynomial-time interior point algorithms using known search directions, namely, the HKM direction, its dual or the NT direction, to solve semi-definite programs (SDPs) is shown by (i) assuming that the given SDP is nondegenerate and making modifications to these algorithms [10], or (ii) considering special classes of SDPs, such as the class of linear semi-definite feasibility problems (LSDFPs) and requiring the initial iterate to the algorithm to satisfy certain conditions [26, 27]. Otherwise, these algorithms are not easy to implement even though they are shown to have polynomial iteration complexities and superlinear convergence [14]. The conditions in [26, 27] that the initial iterate to the algorithm is required to satisfy to have superlinear convergence when solving LSDFPs however are not practical. In this paper, we propose a practical initial iterate to an implementable infeasible interior point algorithm that guarantees superlinear convergence when the algorithm is used to solve the homogeneous feasibility model of an LSDFP.
