On a subproblem of trust region algorithms for constrained optimization
On a subproblem of trust region algorithms for constrained optimization
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DOI：
10.1007/bf01580852
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发表时间：
1990-05
影响因子：
2.7
通讯作者：
Ya-xiang Yuan
中科院分区：
文献类型：
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作者：
Ya-xiang Yuan
研究了等式约束优化信赖域算法中的一个子问题。它是具有两个特殊二次约束的一般二次函数的最小化。给出了这类子问题的性质。证明了拉格朗日的Hessian最多有一个负特征值，并给出了一个例子，说明当一个约束在解处无效时，Hessian可能有一个负特征值。
We study a subproblem that arises in some trust region algorithms for equality constrained optimization. It is the minimization of a general quadratic function with two special quadratic constraints. Properties of such subproblems are given. It is proved that the Hessian of the Lagrangian has at most one negative eigenvalue, and an example is presented to show that the Hessian may have a negative eigenvalue when one constraint is inactive at the solution.