GQTPAR

Computing a trust region step We propose an algorithm for the problem of minimizing a quadratic function subject to an ellipsoidal constraint and show that this algorithm is guaranteed to produce a nearly optimal solution in a finite number of iterations. We also consider the use of this algorithm in a trust region Newton’s method. In particular, we prove that under reasonable assumptions the sequence generated by Newton’s method has a limit point which satisfies the first and second order necessary conditions for a minimizer of the objective function. Numerical results for GQTPAR, which is a Fortran implementation of our algorithm, show that GQTPAR is quite successful in a trust region method. In our tests a call to GQTPAR only required 1.6 iterations on the average.


References in zbMATH (referenced in 315 articles , 1 standard article )

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  1. Curtis, Frank E.; Robinson, Daniel P.; Royer, Clément W.; Wright, Stephen J.: Trust-region Newton-CG with strong second-order complexity guarantees for nonconvex optimization (2021)
  2. Bahrami, Somayeh; Amini, Keyvan: An efficient two-step trust-region algorithm for exactly determined consistent systems of nonlinear equations (2020)
  3. Brás, C. P.; Martínez, J. M.; Raydan, M.: Large-scale unconstrained optimization using separable cubic modeling and matrix-free subspace minimization (2020)
  4. Cartis, Coralia; Gould, Nicholas I. M.; Lange, Marius: On monotonic estimates of the norm of the minimizers of regularized quadratic functions in Krylov spaces (2020)
  5. Daneshmand, Amir; Scutari, Gesualdo; Kungurtsev, Vyacheslav: Second-order guarantees of distributed gradient algorithms (2020)
  6. Erway, Jennifer B.; Griffin, Joshua; Marcia, Roummel F.; Omheni, Riadh: Trust-region algorithms for training responses: machine learning methods using indefinite Hessian approximations (2020)
  7. Gao, Guohua; Jiang, Hao; Vink, Jeroen C.; van Hagen, Paul P. H.; Wells, Terence J.: Performance enhancement of Gauss-Newton trust-region solver for distributed Gauss-Newton optimization method (2020)
  8. Gould, Nicholas I. M.; Simoncini, Valeria: Error estimates for iterative algorithms for minimizing regularized quadratic subproblems (2020)
  9. Jiang, Rujun; Li, Duan: On conic relaxations of generalization of the extended trust region subproblem (2020)
  10. Jiang, Rujun; Li, Duan: A linear-time algorithm for generalized trust region subproblems (2020)
  11. Lieder, Felix: Solving large-scale cubic regularization by a generalized eigenvalue problem (2020)
  12. Milz, Johannes; Ulbrich, Michael: An approximation scheme for distributionally robust nonlinear optimization (2020)
  13. Nguyen, Van-Bong; Nguyen, Thi Ngan; Sheu, Ruey-Lin: Strong duality in minimizing a quadratic form subject to two homogeneous quadratic inequalities over the unit sphere (2020)
  14. Taati, Akram; Salahi, Maziar: On local non-global minimizers of quadratic optimization problem with a single quadratic constraint (2020)
  15. Wang, Jiulin; Xia, Yong: Closing the gap between necessary and sufficient conditions for local nonglobal minimizer of trust region subproblem (2020)
  16. Wang, Li-Yan; Liu, Ji-Jun: On fluorophore imaging by diffusion equation model: decompositions and optimizations (2020)
  17. Wang, Xiaohui; Zhang, Hao; Xia, Yong: GPS localization problem: a new model and its global optimization (2020)
  18. Xu, Peng; Roosta, Fred; Mahoney, Michael W.: Newton-type methods for non-convex optimization under inexact Hessian information (2020)
  19. Zhang, Lei-Hong; Yang, Wei Hong; Shen, Chungen; Ying, Jiaqi: An eigenvalue-based method for the unbalanced Procrustes problem (2020)
  20. Adachi, Satoru; Nakatsukasa, Yuji: Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint (2019)

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