On secant updates for use in general constrained optimization
On secant updates for use in general constrained optimization
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DOI：
10.1090/s0025-5718-1988-0942149-3
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发表时间：
1988-07
影响因子：
2
通讯作者：
R. Tapia
中科院分区：
文献类型：
--
作者：
R. Tapia
本文对等式约束优化问题提出了两类新的逐次二次规划正割方法。一类方法使用SQP增广拉格朗日公式，而另一类使用SQP拉格朗日公式。我们证明，在标准的假设下，在这两种情况下的BFGS和DFP版本的算法是局部q-超线性收敛。据我们所知，这是第一次，无论是本地或q-超线性收敛已被建立的SQP拉格朗日割线方法，使用BFGS或DFP更新哲学，并假设不超过标准的假设。由于标准假设不要求拉格朗日的Hessian在解处的正定性，因此我们的BFGS和DFP更新仅在适当的子空间上具有遗传正定性也就不足为奇了。
In this paper we present two new classes of successive quadratic programming (SQP) secant methods for the equality-constrained optimization problem. One class of methods uses the SQP augmented Lagrangian formulation, while the other class uses the SQP Lagrangian formulation. We demonstrate, under the standard assumptions, that in both cases the BFGS and DFP versions of the algorithm are locally q-superlinearly convergent. To our knowledge this is the first time that either local or q-superlinear convergence has been established for an SQP Lagrangian secant method which uses either the BFGS or DFP updating philosophy and assumes no more than the standard assumptions. Since the standard assumptions do not require positive definiteness of the Hessian of the Lagrangian at the solution, it is no surprise that our BFGS and DFP updates possess the hereditary positive definiteness property only on a proper subspace.