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.

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  1. Adachi, Satoru; Nakatsukasa, Yuji: Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint (2019)
  2. Amiri, Erfan A.; Craig, James R.; Hirmand, M. Reza: A trust region approach for numerical modeling of non-isothermal phase change (2019)
  3. Birgin, E. G.; Martínez, J. M.: A Newton-like method with mixed factorizations and cubic regularization for unconstrained minimization (2019)
  4. Guan, Yu; Chu, Delin: Numerical computation for orthogonal low-rank approximation of tensors (2019)
  5. Huang, Baohua; Ma, Changfeng: The least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint (2019)
  6. Jiang, Rujun; Li, Duan: Novel reformulations and efficient algorithms for the generalized trust region subproblem (2019)
  7. Larson, Jeffrey; Menickelly, Matt; Wild, Stefan M.: Derivative-free optimization methods (2019)
  8. Lee, Ching-pei; Wright, Stephen J.: Inexact successive quadratic approximation for regularized optimization (2019)
  9. Nino-Ruiz, Elias D.; Ardila, Carlos; Estrada, Jesus; Capacho, Jose: A reduced-space line-search method for unconstrained optimization via random descent directions (2019)
  10. Paternain, Santiago; Mokhtari, Aryan; Ribeiro, Alejandro: A Newton-based method for nonconvex optimization with fast evasion of saddle points (2019)
  11. Taati, A.; Salahi, M.: A conjugate gradient-based algorithm for large-scale quadratic programming problem with one quadratic constraint (2019)
  12. Xia, Yong; Wang, Longfei; Yang, Meijia: A fast algorithm for globally solving Tikhonov regularized total least squares problem (2019)
  13. Amaioua, Nadir; Audet, Charles; Conn, Andrew R.; Le Digabel, Sébastien: Efficient solution of quadratically constrained quadratic subproblems within the mesh adaptive direct search algorithm (2018)
  14. Barbero, Álvaro; Sra, Suvrit: Modular proximal optimization for multidimensional total-variation regularization (2018)
  15. Beck, Amir; Vaisbourd, Yakov: Globally solving the trust region subproblem using simple first-order methods (2018)
  16. Bellavia, Stefania; Riccietti, Elisa: On an elliptical trust-region procedure for ill-posed nonlinear least-squares problems (2018)
  17. Bruins, Marianne; Duffy, James A.; Keane, Michael P.; Smith, Anthony A. jun.: Generalized indirect inference for discrete choice models (2018)
  18. Curtis, Frank E.; Robinson, Daniel P.; Samadi, Mohammadreza: Complexity analysis of a trust funnel algorithm for equality constrained optimization (2018)
  19. Dussault, Jean-Pierre: ARC(_q): a new adaptive regularization by cubics (2018)
  20. Guan, Yu; Chu, Moody T.; Chu, Delin: Convergence analysis of an SVD-based algorithm for the best rank-1 tensor approximation (2018)

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