# An efficient algorithm for solving the generalized trust region subproblem

## Abstract

In this paper, we consider the interval bounded generalized trust region subproblem (GTRS) which is the problem of minimizing a general quadratic function subject to an upper and lower bounded general quadratic constraint. Under the assumption that two matrices from the objective and the constraint functions can be simultaneously diagonalizable via congruence, a diagonalization-based algorithm is introduced to solve it by showing that GTRS is indeed equivalent to a linearly constrained convex univariate problem. Some numerical experiments are given to show the effectiveness of the proposed method and to compare it with the extended Rendl–Wolkowicz algorithm due to Pong and Wolkowicz.

- Authors:

- University of Guilan, Faculty of Mathematical Sciences (Iran, Islamic Republic of)

- Publication Date:

- OSTI Identifier:
- 22769382

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; FUNCTIONS; MATRICES; OPTIMIZATION

### Citation Formats

```
Salahi, M., E-mail: salahim@guilan.ac.ir, and Taati, A.
```*An efficient algorithm for solving the generalized trust region subproblem*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0349-1.

```
Salahi, M., E-mail: salahim@guilan.ac.ir, & Taati, A.
```*An efficient algorithm for solving the generalized trust region subproblem*. United States. doi:10.1007/S40314-016-0349-1.

```
Salahi, M., E-mail: salahim@guilan.ac.ir, and Taati, A. Thu .
"An efficient algorithm for solving the generalized trust region subproblem". United States. doi:10.1007/S40314-016-0349-1.
```

```
@article{osti_22769382,
```

title = {An efficient algorithm for solving the generalized trust region subproblem},

author = {Salahi, M., E-mail: salahim@guilan.ac.ir and Taati, A.},

abstractNote = {In this paper, we consider the interval bounded generalized trust region subproblem (GTRS) which is the problem of minimizing a general quadratic function subject to an upper and lower bounded general quadratic constraint. Under the assumption that two matrices from the objective and the constraint functions can be simultaneously diagonalizable via congruence, a diagonalization-based algorithm is introduced to solve it by showing that GTRS is indeed equivalent to a linearly constrained convex univariate problem. Some numerical experiments are given to show the effectiveness of the proposed method and to compare it with the extended Rendl–Wolkowicz algorithm due to Pong and Wolkowicz.},

doi = {10.1007/S40314-016-0349-1},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 1,

volume = 37,

place = {United States},

year = {2018},

month = {3}

}

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