Algorithm 813: SPG—Software for Convex-Constrained Optimization
ACM Transactions on Mathematical Software (TOMS)
Algorithm 873: LSTRS: MATLAB software for large-scale trust-region subproblems and regularization
ACM Transactions on Mathematical Software (TOMS)
A modified trust region method with Beale's PCG technique for optimization
Computational Optimization and Applications
Improved spectral relaxation methods for binary quadratic optimization problems
Computer Vision and Image Understanding
Image segmentation with context
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
A Subspace Minimization Method for the Trust-Region Step
SIAM Journal on Optimization
Accelerating the LSTRS Algorithm
SIAM Journal on Scientific Computing
Lagrangian Duality and Branch-and-Bound Algorithms for Optimal Power Flow
Operations Research
Simultaneous multiple rotation averaging using lagrangian duality
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part III
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An important problem in linear algebra and optimization is the trust-region subproblem: minimize a quadratic function subject to an ellipsoidal or spherical constraint. This basic problem has several important large-scale applications including seismic inversion and forcing convergence in optimization methods. Existing methods to solve the trust-region subproblem require matrix factorizations, which are not feasible in the large-scale setting. This paper presents an algorithm for solving the large-scale trust-region subproblem that requires a fixed-size limited storage proportional to the order of the quadratic and that relies only on matrix-vector products. The algorithm recasts the trust-region subproblem in terms of a parameterized eigenvalue problem and adjusts the parameter with a superlinearly convergent iteration to find the optimal solution from the eigenvector of the parameterized problem. Only the smallest eigenvalue and corresponding eigenvector of the parameterized problem needs to be computed. The implicitly restarted Lanczos method is well suited to this subproblem.