A TRUST REGION ALGORITHM FOR NONLINEARLY CONSTRAINED OPTIMIZATION
A TRUST REGION ALGORITHM FOR NONLINEARLY CONSTRAINED OPTIMIZATION
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DOI：
10.1137/0724076
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发表时间：
1987-10-01
影响因子：
2.9
通讯作者：
SHULTZ, GA
中科院分区：
文献类型：
--
作者：
BYRD, RH;SCHNABEL, RB;SHULTZ, GA
针对一般非线性等式约束优化问题，提出了一种基于信赖域的求解方法。该方法的工作原理是通过迭代最小化的拉格朗日二次模型的问题约束和信赖域约束的可能放松的线性化。模型最小化可以用狗腿型方法近似地完成。证明了该方法在奇异或不定Hessian近似下的全局收敛性，并给出了一个二阶修正步骤，使迭代过程更接近可行集.如果使用足够精确的Hessian信息，这个校正步骤允许我们证明该方法也是局部二次收敛的，并且极限满足约束优化的二阶必要条件。一个例子表明，如果没有这种校正，可能会出现类似于Maratos效应的情况下，迭代无法远离鞍点。
We present a trust region-based method for the general nonlinearly equality constrained optimization problem. The method works by iteratively minimizing a quadratic model of the Lagrangian subject to a possibly relaxed linearization of the problem constraints and a trust region constraint. The model minimization may be done approximately with a dogleg-type approach. We show that this method is globally convergent even if singular or indefinite Hessian approximations are made.A second order correction step that brings the iterates closer to the feasible set is described. If sufficiently precise Hessian information is used, this correction step allows us to prove that the method is also locally quadratically convergent, and that the limit satisfies the second order necessary conditions for constrained optimization. An example is given to show that, without this correction, a situation similar to the Maratos effect may occur where the iteration is unable to move away from a saddle point.