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.
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References in zbMATH (referenced in 294 articles , 1 standard article )
Showing results 1 to 20 of 294.
Sorted by year (- Adachi, Satoru; Nakatsukasa, Yuji: Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint (2019)
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- Huang, Baohua; Ma, Changfeng: The least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint (2019)
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- Paternain, Santiago; Mokhtari, Aryan; Ribeiro, Alejandro: A Newton-based method for nonconvex optimization with fast evasion of saddle points (2019)
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- Xia, Yong; Wang, Longfei; Yang, Meijia: A fast algorithm for globally solving Tikhonov regularized total least squares problem (2019)
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- Barbero, Álvaro; Sra, Suvrit: Modular proximal optimization for multidimensional total-variation regularization (2018)
- Beck, Amir; Vaisbourd, Yakov: Globally solving the trust region subproblem using simple first-order methods (2018)
- Bellavia, Stefania; Riccietti, Elisa: On an elliptical trust-region procedure for ill-posed nonlinear least-squares problems (2018)
- Bruins, Marianne; Duffy, James A.; Keane, Michael P.; Smith, Anthony A. jun.: Generalized indirect inference for discrete choice models (2018)
- Curtis, Frank E.; Robinson, Daniel P.; Samadi, Mohammadreza: Complexity analysis of a trust funnel algorithm for equality constrained optimization (2018)
- Dussault, Jean-Pierre: ARC(_q): a new adaptive regularization by cubics (2018)
- Guan, Yu; Chu, Moody T.; Chu, Delin: Convergence analysis of an SVD-based algorithm for the best rank-1 tensor approximation (2018)