Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure o
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on ...
Absil, P.-A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton (2009) MATHGoogle Scholar Absil, P.-A., Malick, J.: Projection-like retractions on matrix manifolds. SIAM J. Optim.22, 135–158 (2012) MathSciNetMATHGoogle Schol...
There exists a large body of work on the problem of computing the geometric matrix means [30]. Classic algorithms like Newton’s method or Gradient Decent (GD) have been successfully applied to the problem. Standard toolboxes implement efficient variations of GD like Steppest Decent or Conjugate...
The geometry of algorithms with orthogonality constraints SIAM Journal on Matrix Analysis and Applications, 20 (2) (1998), pp. 303-353, 10.1137/S0895479895290954 View in ScopusGoogle Scholar Eldén and Park, 1999 L. Eldén, H. Park A Procrustes problem on the Stiefel manifold Numerische Mathemati...
Optimization Algorithms on Matrix Manifolds byP.-A. Absil, R. Mahony, R. Sepulchre-Princeton University Press,2007 Many science and engineering problems can be rephrased as optimization problems on matrix search spaces endowed with a manifold structure. This book shows how to exploit the structure...
Note that various manifold algrithms on various manifolds are implemented in MATLAB toolbox manopt. The RSOpt codes are compliant to manopt. Also, please see here for more comprehensive explanation of optimization algorithms on matrix manifolds....
In: Optimization algorithms on matrix manifolds. Princeton: Princeton University Press; 2009. 29. Liu H, So AMC, Wu W. Quadratic optimization with orthogonality constraint: explicit Łojasiewicz exponent and linear convergence of retraction-based line-search and stochastic variance-reduced gradient ...
May 1, 2024|research areaMethods and Algorithms|conferenceICLR We present Manifold Diffusion Fields (MDF), an approach that unlocks learning of diffusion models of data in general non-euclidean geometries. Leveraging insights from spectral geometry analysis, we define an intrinsic coordinate system on ...
Optimization Algorithms on Matrix Manifolds; Princeton University Press: Princeton, NJ, USA, 2008. [Google Scholar] Bento, G.C.; Ferreira, O.P.; Oliveira, P.R. Proximal point method for a special class of nonconvex functions on Hadamard manifolds. Optim. J. Math. Program. Oper. Res. ...