An interior trust region approach for nonlinear minimization subject to bounds
An interior trust region approach for nonlinear minimization subject to bounds
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DOI：
10.1137/0806023
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发表时间：
1996-05-01
影响因子：
3.1
通讯作者：
Li, YY
中科院分区：
文献类型：
--
作者：
Coleman, TF;Li, YY
我们提出了一种新的信任域方法来最小化具有简单边界的非线性函数。与大多数现有方法不同，我们提出的方法不需要在每次迭代中求解具有不等式约束的二次规划子问题。相反，信任域子问题的解是通过最小化仅受椭球体约束的二次函数来定义的。生成的迭代是严格可行的。对于变量没有上界和下界的无约束问题，本文提出的方法可以简化为标准的信赖域方法。建立了全局和局部二次收敛性。初步的数值实验表明了这种方法的实际可行性。
We propose a new trust region approach for minimizing a nonlinear function subject to simple bounds. Unlike most existing methods, our proposed method does not require that a quadratic programming subproblem, with inequality constraints, be solved in each iteration. Instead, a solution to a trust region subproblem is defined by minimizing a quadratic function subject only to an ellipsoidal constraint. The iterates generated are strictly feasible. Our proposed method reduces to a standard trust region approach for the unconstrained problem when there are no upper or lower bounds on the variables. Global and local quadratic convergence is established. Preliminary numerical experiments are reported indicating the practical viability of this approach.