A framework of constraint preserving update schemes for optimization on Stiefel manifold
From MaRDI portal
Publication:747775
DOI10.1007/s10107-014-0816-7zbMath1325.49037arXiv1301.0172OpenAlexW2106173883MaRDI QIDQ747775
Publication date: 19 October 2015
Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1301.0172
optimizationStiefel manifoldfeasibilitylow-rank correlation matrixorthogonality constraintadaptive nonmonotone line searchBarzilai-Borwein-like methodheterogeneous quadratic functionsKohn-Sham total energy minimizationsphere constraintupdate schemes
Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Numerical methods based on nonlinear programming (49M37) Manifolds and measure-geometric topics (49Q99)
Related Items (44)
Smoothing projected Barzilai-Borwein method for constrained non-Lipschitz optimization ⋮ A smoothing SQP framework for a class of composite \(L_q\) minimization over polyhedron ⋮ Adaptive Quadratically Regularized Newton Method for Riemannian Optimization ⋮ A class of smooth exact penalty function methods for optimization problems with orthogonality constraints ⋮ Stochastic consensus dynamics for nonconvex optimization on the Stiefel manifold: Mean-field limit and convergence ⋮ Riemannian conjugate gradient methods for computing the extreme eigenvalues of symmetric tensors ⋮ Multiple graphs clustering by gradient flow method ⋮ Nonconvex and nonsmooth optimization with generalized orthogonality constraints: an approximate augmented Lagrangian method ⋮ Nonmonotone inexact restoration approach for minimization with orthogonality constraints ⋮ Implicit steepest descent algorithm for optimization with orthogonality constraints ⋮ The abstract Laplacian tensor of a hypergraph with applications in clustering ⋮ A regularized Newton method for computing ground states of Bose-Einstein condensates ⋮ Jacobi-type algorithms for homogeneous polynomial optimization on Stiefel manifolds with applications to tensor approximations ⋮ A competitive optimization approach for data clustering and orthogonal non-negative matrix factorization ⋮ The Fiedler Vector of a Laplacian Tensor for Hypergraph Partitioning ⋮ Non-monotone inexact restoration method for nonlinear programming ⋮ Nonmonotone feasible arc search algorithm for minimization on Stiefel manifold ⋮ A Conjugate Gradient Method for Electronic Structure Calculations ⋮ A penalty-free infeasible approach for a class of nonsmooth optimization problems over the Stiefel manifold ⋮ A communication-efficient and privacy-aware distributed algorithm for sparse PCA ⋮ A Block Lanczos Method for Large-Scale Quadratic Minimization Problems with Orthogonality Constraints ⋮ A collection of efficient retractions for the symplectic Stiefel manifold ⋮ Generalized left-localized Cayley parametrization for optimization with orthogonality constraints ⋮ A New First-Order Algorithmic Framework for Optimization Problems with Orthogonality Constraints ⋮ On the generalized essential matrix correction: an efficient solution to the problem and its applications ⋮ A brief introduction to manifold optimization ⋮ Orthogonal canonical correlation analysis and applications ⋮ Hypergraph Clustering Using a New Laplacian Tensor with Applications in Image Processing ⋮ Gradient Flow Based Kohn--Sham Density Functional Theory Model ⋮ Solving the discrete Euler-Arnold equations for the generalized rigid body motion ⋮ A Filter Active-Set Algorithm for Ball/Sphere Constrained Optimization Problem ⋮ First order optimality conditions and steepest descent algorithm on orthogonal Stiefel manifolds ⋮ A Riemannian conjugate gradient method for optimization on the Stiefel manifold ⋮ Cheeger's cut, maxcut and the spectral theory of 1-Laplacian on graphs ⋮ Proximal Gradient Method for Nonsmooth Optimization over the Stiefel Manifold ⋮ A framework of constraint preserving update schemes for optimization on Stiefel manifold ⋮ An inexact augmented Lagrangian method for computing strongly orthogonal decompositions of tensors ⋮ An alternate gradient method for optimization problems with orthogonality constraints ⋮ On matrix exponentials and their approximations related to optimization on the Stiefel manifold ⋮ Parallelizable Algorithms for Optimization Problems with Orthogonality Constraints ⋮ Delta invariant for Eulerian digraphs ⋮ Quadratic optimization with orthogonality constraint: explicit Łojasiewicz exponent and linear convergence of retraction-based line-search and stochastic variance-reduced gradient methods ⋮ An Eigenvalue-Based Method for the Unbalanced Procrustes Problem ⋮ Exact Penalty Function for $\ell_{2,1}$ Norm Minimization over the Stiefel Manifold
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A feasible method for optimization with orthogonality constraints
- An alternating variable method for the maximal correlation problem
- Folding-free global conformal mapping for genus-0 surfaces by harmonic energy minimization
- An inexact interior point method for \(L_{1}\)-regularized sparse covariance selection
- A framework of constraint preserving update schemes for optimization on Stiefel manifold
- Gradient methods with adaptive step-sizes
- Efficient rank reduction of correlation matrices
- Conjugate gradient algorithm for optimization under unitary matrix constraint
- Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints
- Extrema of sums of heterogeneous quadratic forms
- Some global optimization problems on Stiefel manifolds
- Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming
- A Procrustes problem on the Stiefel manifold
- On minimization on Stiefel manifolds
- New algorithms for singly linearly constrained quadratic programs subject to lower and upper bounds
- Optimization theory and methods. Nonlinear programming
- A constrained optimization algorithm for total energy minimization in electronic structure calculations
- A generalized solution of the orthogonal Procrustes problem
- Richtungsfelder und Fernparallelismus in \(n\)-dimensionalen Mannigfaltigkeiten
- R-linear convergence of the Barzilai and Borwein gradient method
- Feasible Barzilai–Borwein-like methods for extreme symmetric eigenvalue problems
- Generalized power method for sparse principal component analysis
- Projection-like Retractions on Matrix Manifolds
- KSSOLV—a MATLAB toolbox for solving the Kohn-Sham equations
- The university of Florida sparse matrix collection
- The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
- A Sequential Semismooth Newton Method for the Nearest Low-rank Correlation Matrix Problem
- A Quadratically Convergent Newton Method for Computing the Nearest Correlation Matrix
- A Trust Region Direct Constrained Minimization Algorithm for the Kohn–Sham Equation
- On Augmented Lagrangian Methods with General Lower-Level Constraints
- Two-Point Step Size Gradient Methods
- The Geometry of Algorithms with Orthogonality Constraints
- Nonmonotone Spectral Projected Gradient Methods on Convex Sets
- Steepest Descent Algorithms for Optimization Under Unitary Matrix Constraint
- Rank reduction of correlation matrices by majorization
- A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization
- A Nonmonotone Line Search Technique for Newton’s Method
- An Inexact Accelerated Proximal Gradient Method for Large Scale Linearly Constrained Convex SDP
- Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors
- On the Barzilai and Borwein choice of steplength for the gradient method
- Optimization algorithms exploiting unitary constraints
- The cyclic Barzilai-–Borwein method for unconstrained optimization
- A Direct Formulation for Sparse PCA Using Semidefinite Programming
- Adaptive two-point stepsize gradient algorithm
This page was built for publication: A framework of constraint preserving update schemes for optimization on Stiefel manifold
