Local superlinear and quadratic convergence of RSSQP

Establish local superlinear and quadratic convergence of the proposed stabilized Riemannian sequential quadratic programming (RSSQP) method for Riemannian nonlinear programming problems with equality and inequality constraints under suitable second-order and regularity assumptions.

Background

The paper develops the RSSQP method for degenerate constrained optimization problems on Riemannian manifolds and proves a global convergence result: under boundedness and the stated assumptions, an accumulation point is a KKT point, an AKKT point, or a stationary point of an associated feasibility problem. The paper does not establish local convergence rates for the method.

The unresolved direction is to determine whether, and under which suitable second-order and regularity assumptions, the RSSQP iterates exhibit local superlinear or quadratic convergence. Such results would complement the existing global convergence characterization with fast local convergence guarantees.