Generalized equations and their solutions, Part I: Basic theory
Generalized equations and their solutions, Part I: Basic theory
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DOI：
10.1007/bfb0120850
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发表时间：
1979
期刊：
影响因子：
--
通讯作者：
S. M. Robinson
中科院分区：
文献类型：
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作者：
S. M. Robinson
我们考虑一类“广义方程”，涉及点到集的映射，其中制定的线性和非线性规划和互补问题，等等。这种广义方程的解集在一定的假设下是稳定的，特别是一个一般形式的隐函数定理证明了这类问题。本文最后给出了线性广义方程的一个应用，包括线性和凸二次规划以及半正定线性互补问题。一般的非线性规划问题的处理在第二部分的文件，使用这里开发的方法。
We consider a class of “generalized equations,” involving point-to-set mappings, which formulate the problems of linear and nonlinear programming and of complementarity, among others. Solution sets of such generalized equations are shown to be stable under certain hypotheses; in particular a general form of the implicit function theorem is proved for such problems. An application to linear generalized equations is given at the end of the paper; this covers linear and convex quadratic programming and the positive semidefinite linear complementarity problem. The general nonlinear programming problem is treated in Part II of the paper, using the methods developed here.