# Jordan-Algebraic Aspects of Nonconvex Optimization over Symmetric Cones

## Abstract

We illustrate the usefulness of Jordan-algebraic techniques for nonconvex optimization by considering a potential-reduction algorithm for a nonconvex quadratic function over the domain obtained as the intersection of a symmetric cone with an affine subspace.

- Authors:

- Department of Mathematics, University of Notre Dame, 255 Hurley Hall, Notre Dame, IN 46556 (United States), E-mail: ylu4@nd.edu

- Publication Date:

- OSTI Identifier:
- 21064214

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Applied Mathematics and Optimization; Journal Volume: 53; Journal Issue: 1; Other Information: DOI: 10.1007/s00245-005-0835-0; Copyright (c) 2006 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CONES; FUNCTIONS; OPTIMIZATION; POTENTIALS

### Citation Formats

```
Faybusovich, Leonid, E-mail: leonid.faybusovich.1@nd.edu, and Lu Ye.
```*Jordan-Algebraic Aspects of Nonconvex Optimization over Symmetric Cones*. United States: N. p., 2006.
Web. doi:10.1007/S00245-005-0835-0.

```
Faybusovich, Leonid, E-mail: leonid.faybusovich.1@nd.edu, & Lu Ye.
```*Jordan-Algebraic Aspects of Nonconvex Optimization over Symmetric Cones*. United States. doi:10.1007/S00245-005-0835-0.

```
Faybusovich, Leonid, E-mail: leonid.faybusovich.1@nd.edu, and Lu Ye. Sun .
"Jordan-Algebraic Aspects of Nonconvex Optimization over Symmetric Cones". United States.
doi:10.1007/S00245-005-0835-0.
```

```
@article{osti_21064214,
```

title = {Jordan-Algebraic Aspects of Nonconvex Optimization over Symmetric Cones},

author = {Faybusovich, Leonid, E-mail: leonid.faybusovich.1@nd.edu and Lu Ye},

abstractNote = {We illustrate the usefulness of Jordan-algebraic techniques for nonconvex optimization by considering a potential-reduction algorithm for a nonconvex quadratic function over the domain obtained as the intersection of a symmetric cone with an affine subspace.},

doi = {10.1007/S00245-005-0835-0},

journal = {Applied Mathematics and Optimization},

number = 1,

volume = 53,

place = {United States},

year = {Sun Jan 15 00:00:00 EST 2006},

month = {Sun Jan 15 00:00:00 EST 2006}

}

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