Algorithm 813: SPG—Software for Convex-Constrained Optimization
ACM Transactions on Mathematical Software (TOMS)
Computational Optimization and Applications
Algorithm 873: LSTRS: MATLAB software for large-scale trust-region subproblems and regularization
ACM Transactions on Mathematical Software (TOMS)
Nonnegative matrix factorization with quadratic programming
Neurocomputing
Trust-region interior-point method for large sparse l1 optimization
Optimization Methods & Software
Improved spectral relaxation methods for binary quadratic optimization problems
Computer Vision and Image Understanding
Solving the quadratic trust-region subproblem in a low-memory BFGS framework
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART I
CARD: a decision-guidance framework and application for recommending composite alternatives
Proceedings of the 2008 ACM conference on Recommender systems
BFGS trust-region method for symmetric nonlinear equations
Journal of Computational and Applied Mathematics
Image segmentation with context
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
An iterative Lagrange method for the regularization of discrete ill-posed inverse problems
Computers & Mathematics with Applications
A Subspace Minimization Method for the Trust-Region Step
SIAM Journal on Optimization
Accelerating the LSTRS Algorithm
SIAM Journal on Scientific Computing
Behavior of DCA sequences for solving the trust-region subproblem
Journal of Global Optimization
Lagrangian Duality and Branch-and-Bound Algorithms for Optimal Power Flow
Operations Research
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We present a new method for the large-scale trust-region subproblem. The method is matrix-free in the sense that only matrix-vector products are required. We recast the trust-region subproblem as a parameterized eigenvalue problem and compute an optimal value for the parameter. We then find the solution of the trust-region subproblem from the eigenvectors associated with two of the smallest eigenvalues of the parameterized eigenvalue problem corresponding to the optimal parameter. The new algorithm uses a different interpolating scheme than existing methods and introduces a unified iteration that naturally includes the so-called hard case. We show that the new iteration is well defined and convergent at a superlinear rate. We present computational results to illustrate convergence properties and robustness of the method.