Global Optimization with Orthogonality Constraints via Stochastic Diffusion on Manifold

[1]  Michael Ulbrich,et al.  On the Analysis of the Discretized Kohn-Sham Density Functional Theory , 2014, SIAM J. Numer. Anal..

[2]  Jian-Feng Cai,et al.  Data-driven tight frame construction and image denoising , 2014 .

[3]  Lok Ming Lui,et al.  Folding-Free Global Conformal Mapping for Genus-0 Surfaces by Harmonic Energy Minimization , 2013, Journal of Scientific Computing.

[4]  Wotao Yin,et al.  A feasible method for optimization with orthogonality constraints , 2013, Math. Program..

[5]  S. Osher,et al.  Compressed modes for variational problems in mathematics and physics , 2013, Proceedings of the National Academy of Sciences.

[6]  Michael Ulbrich,et al.  Adaptive Regularized Self-Consistent Field Iteration with Exact Hessian for Electronic Structure Calculation , 2013, SIAM J. Sci. Comput..

[7]  Shui-Nee Chow,et al.  Global Optimizations by Intermittent Diffusion , 2013 .

[8]  Wotao Yin,et al.  Trust, But Verify: Fast and Accurate Signal Recovery From 1-Bit Compressive Measurements , 2011, IEEE Transactions on Signal Processing.

[9]  Yoel Shkolnisky,et al.  Three-Dimensional Structure Determination from Common Lines in Cryo-EM by Eigenvectors and Semidefinite Programming , 2011, SIAM J. Imaging Sci..

[10]  Anuj Srivastava,et al.  Optimal linear projections for enhancing desired data statistics , 2010, Stat. Comput..

[11]  Berç Rustem,et al.  Convergence analysis of a global optimization algorithm using stochastic differential equations , 2009, J. Glob. Optim..

[12]  Chen Ling,et al.  Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations , 2009, SIAM J. Optim..

[13]  Berç Rustem,et al.  An Algorithm for the Global Optimization of a Class of Continuous Minimax Problems , 2009 .

[14]  Berç Rustem,et al.  Global optimization of robust chance constrained problems , 2009, J. Glob. Optim..

[15]  Levent Tunçel,et al.  Optimization algorithms on matrix manifolds , 2009, Math. Comput..

[16]  Wotao Yin,et al.  A Curvilinear Search Method for p-Harmonic Flows on Spheres , 2009, SIAM J. Imaging Sci..

[17]  Richard G. Baraniuk,et al.  1-Bit compressive sensing , 2008, 2008 42nd Annual Conference on Information Sciences and Systems.

[18]  Simon J. A. Malham,et al.  Stochastic Lie Group Integrators , 2007, SIAM J. Sci. Comput..

[19]  Shrawan Kumar,et al.  Differential Geometry and its Applications , 2007 .

[20]  George Yin,et al.  Global Optimization Using Diffusion Perturbations with Large Noise Intensity , 2006 .

[21]  Berç Rustem,et al.  Linearly Constrained Global Optimization and Stochastic Differential Equations , 2006, J. Glob. Optim..

[22]  Oliver Henkel,et al.  Sphere-packing bounds in the Grassmann and Stiefel manifolds , 2003, IEEE Transactions on Information Theory.

[23]  A. Bruckstein,et al.  K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation , 2005 .

[24]  E. Hairer,et al.  Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations , 2004 .

[25]  Anuj Srivastava,et al.  Optimal linear representations of images for object recognition , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[26]  C. Villani,et al.  ON THE TREND TO EQUILIBRIUM FOR THE FOKKER-PLANCK EQUATION : AN INTERPLAY BETWEEN PHYSICS AND FUNCTIONAL ANALYSIS , 2004 .

[27]  Anuj Srivastava,et al.  Stochastic Search for Optimal Linear Representations of Images on Spaces with Orthogonality Constraints , 2003, EMMCVPR.

[28]  S. Yau,et al.  Global conformal surface parameterization , 2003 .

[29]  Stanley Osher,et al.  Numerical Methods for p-Harmonic Flows and Applications to Image Processing , 2002, SIAM J. Numer. Anal..

[30]  Guillermo Sapiro,et al.  Color image enhancement via chromaticity diffusion , 2001, IEEE Trans. Image Process..

[31]  Stephen J. Wright,et al.  Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , 2000 .

[32]  Franz Rendl,et al.  A Spectral Bundle Method for Semidefinite Programming , 1999, SIAM J. Optim..

[33]  A. Edelman,et al.  The Geometry of Algorithms with Orthogonality Constraints , 1998, SIAM J. Matrix Anal. Appl..

[34]  H. Munthe-Kaas.  Runge-Kutta methods on Lie groups , 1998 .

[35]  San-Yih Lin,et al.  Relaxation methods for liquid crystal problems , 1989 .

[36]  J. Borwein,et al.  Two-Point Step Size Gradient Methods , 1988 .

[37]  C. Hwang,et al.  Diffusion for global optimization in R n , 1987 .

[38]  B. Gidas.  Global optimization via the Langevin equation , 1985, 1985 24th IEEE Conference on Decision and Control.

[39]  F. Aluffi-Pentini,et al.  Global optimization and stochastic differential equations , 1985 .

[40]  R. L. Stratonovich.  A New Representation for Stochastic Integrals and Equations , 1966 .

[41]  T. Motzkin,et al.  Maxima for Graphs and a New Proof of a Theorem of Turán , 1965, Canadian Journal of Mathematics.

[42]  Stuart GEMANf.  DIFFUSIONS FOR GLOBAL OPTIMIZATION , 2022 .