An SQP Method for Equality Constrained Optimization on Hilbert Manifolds
Speaker: Prof. Dr. Anton Schiela
Affiliation: Universität Bayreuth
Abstract: We extend a sequential quadratic programming method for equality
constrained optimization to the setting of Hilbert manifolds. The use of
retractions and stratifications allow us to pull back the functional
and the constraint mapping to linear spaces and then linearize the
problem. 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 and show transition to fast local
convergence. We test our method on equilibrium problem in elasticity where an
inextensible elastic rod under dead loads is simulated. Then we present
an optimal control problem for this model.