- DIRECT SEARCH ALGORITHMS OVER RIEMANNIAN MANIFOLDS David W. Dreisigmeyer (dreisigmlanl.gov) Abstract: We generalize the Nelder-Mead simplex and LTMADS algorithms and, the frame based methods for function minimization to Riemannian manifolds. Examples are given for functions defined on the special orthogonal Lie group $\mathcal{SO}(n)$ and the Grassmann manifold $\mathcal{G}(n,k)$. Our main examples are applying the generalized LTMADS algorithm to equality constrained optimization problems and, to the Whitney embedding problem for dimensionality reduction of data. A convergence analysis of the frame based method is also given. Keywords: Direct search methods, Riemannian manifolds, Grassmann manifolds, equality constraints, geodesics Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization ) Citation: Download: [PDF]Entry Submitted: 08/02/2007Entry Accepted: 08/02/2007Entry Last Modified: 08/02/2007Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.