Numerical Optimization
Numerical Optimization
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DOI：
10.1007/b98874
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发表时间：
2018-09
期刊：
影响因子：
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通讯作者：
J. Nocedal;Stephen J. Wright
中科院分区：
文献类型：
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作者：
J. Nocedal;Stephen J. Wright
求解非线性约束最优化问题的一个最有效的方法是通过求解二次子问题来生成步长。这种序列二次规划（SQP）方法可以用于线搜索和信赖域框架，它是适合于小或大的问题。与序列线性约束方法（第17章）不同，序列线性约束方法在大多数约束是线性的情况下是有效的，SQP方法在解决具有显著非线性的问题时显示出其优势。我们的SQP方法的开发将分两个阶段进行。首先，我们将提出一个本地算法，激励SQP方法，并允许我们在一个简单的设置中引入步长计算和Hessian近似技术。然后，我们考虑实际的线搜索和信赖域方法，实现从远程起点收敛。
One of the most effective methods for nonlinearly constrained optimization generates steps by solving quadratic subproblems. This sequential quadratic programming (SQP) approach can be used both in line search and trust-region frameworks, and it is appropriate for small or large problems. Unlike sequential linearly constrained methods (Chapter 17), which are effective when most of the constraints are linear, SQP methods show their strength when solving problems with significant nonlinearities. Our development of SQP methods will be done in two stages. First we will present a local algorithm that motivates the SQP approach and that allows us to introduce the step computation and Hessian approximation techniques in a simple setting. We then consider practical line search and trust-region methods that achieve convergence from remote starting points.