论文标题
SQP方法，用于限制对流形的优化
An SQP method for equality constrained optimization on manifolds
论文作者
论文摘要
我们将平等限制优化的SQP方法的类别扩展到可区分歧管的设置。缩回和分层的使用使我们能够将所涉及的映射撤回到线性空间。我们研究局部二次收敛到最小化器。此外，我们提出了一种基于目标函数的立方正规化和仿射协变量的牛顿方法的综合步骤方法。我们显示了该方案快速局部收敛的过渡。我们测试了有限弹性中的平衡问题的方法，其中寻求在死负荷下不可扩展的横向各向同性弹性杆的稳定平衡位置。
We extend the class of SQP methods for equality constrained optimization to the setting of differentiable manifolds. The use of retractions and stratifications allows us to pull back the involved mappings to linear spaces. We study local quadratic convergence to minimizers. In addition we present a composite step method for globalization based on cubic regularization of the objective function and affine covariant damped Newton method for feasibility. We show transition to fast local convergence of this scheme. We test our method on equilibrium problems in finite elasticity where the stable equilibrium position of an inextensible transversely isotropic elastic rod under dead load is sought.
