Sequential Quadratic Optimization for Nonlinear Optimization Problems on Riemannian Manifolds

We consider optimization problems on Riemannian manifolds with equality and inequality constraints, which we call nonlinear (RNLO) problems. Although they have numerous applications, the existing studies them are limited especially in terms of algorithms. In this paper, propose sequential quadratic (RSQO) that uses a line-search technique an $\ell_{1}$ penalty function as extension standard SQO algorithm for constrained Euclidean spaces to manifolds. prove its global convergence Karush--Kuhn--Tucker point RNLO problem by means parallel transport exponential mapping. Furthermore, establish local analyzing relationship between sequences generated RSQO Newton method. Ours is first has both properties Empirical results show finds solutions more stably higher accuracy compared augmented Lagrangian methods.