Homotopy methods are powerful tools for solving nonlinear programming. Their global convergence can be generally established under conditions of the nonemptiness and boundness of the interior of the feasible set, the Positive Linear Independent Constraint Qualification (PLICQ), which is equivalent to the Mangasarian-Fromovitz Constraint Qualification (MFCQ), and the normal cone condition. This paper provides a comparison of the existing normal cone conditions used in homotopy methods for solving inequality constrained nonlinear programming.

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求解不等式约束非线性规划问题的同伦方法的正圆锥条件的比较

同伦方法是解决非线性规划的有力工具。通常可以在可行集内部的非空和有界，正线性独立约束资格（PLICQ）（等同于Mangasarian-Fromovitz约束资格（MFCQ））和法线锥的条件下建立它们的全局收敛性。健康）状况。本文提供了用于解决不等式约束非线性规划的同伦方法中现有法线锥条件的比较。