An SQP method for equality constrained optimization on manifolds

2020/05/14 by Anton Schiela, Schiela, Anton, Julián Ortiz +1 · 1 citation
Engineering · Mathematics · #49M37 #90C06 #90C55 #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Robotic Mechanisms and Dynamics

paper · pdf · doi:10.48550/arxiv.2005.06844

openalex publication_date 2020/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Numerical optimization

Cited by

• Riemannian Direct Trajectory Optimization of Rigid Bodies on Matrix Lie Groups

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