# A Dynamical Systems Analysis of Semidefinite Programming with Application to Quadratic Optimization with Pure Quadratic Equality Constraints

## Abstract

This paper considers the problem of minimizing a quadratic cost subject to purely quadratic equality constraints. This problem is tackled by first relating it to a standard semidefinite programming problem. The approach taken leads to a dynamical systems analysis of semidefinite programming and the formulation of a gradient descent flow which can be used to solve semidefinite programming problems. Though the reformulation of the initial problem as a semidefinite pro- gramming problem does not in general lead directly to a solution of the original problem, the initial problem is solved by using a modified flow incorporating a penalty function.

- Authors:

- Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC 3052 (Australia)
- Heudiasyc - UTC UMR 6599, Centre de Recherche de Royallieu, BP 20529, 60205 Compiegne Cedex (France)
- Department of Systems Engineering, RSISE, Australian National University, Canberra, ACT 0200 (Australia)

- Publication Date:

- OSTI Identifier:
- 21067542

- Resource Type:
- Journal Article

- Journal Name:
- Applied Mathematics and Optimization

- Additional Journal Information:
- Journal Volume: 40; Journal Issue: 2; Other Information: DOI: 10.1007/s002459900122; Copyright (c) 1999 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 1999 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FUNCTIONS; MATHEMATICAL SOLUTIONS; OPTIMIZATION; PROGRAMMING; SYSTEMS ANALYSIS

### Citation Formats

```
Orsi, R. J., Mahony, R. E., and Moore, J. B.
```*A Dynamical Systems Analysis of Semidefinite Programming with Application to Quadratic Optimization with Pure Quadratic Equality Constraints*. United States: N. p., 1999.
Web. doi:10.1007/S002459900122.

```
Orsi, R. J., Mahony, R. E., & Moore, J. B.
```*A Dynamical Systems Analysis of Semidefinite Programming with Application to Quadratic Optimization with Pure Quadratic Equality Constraints*. United States. doi:10.1007/S002459900122.

```
Orsi, R. J., Mahony, R. E., and Moore, J. B. Wed .
"A Dynamical Systems Analysis of Semidefinite Programming with Application to Quadratic Optimization with Pure Quadratic Equality Constraints". United States. doi:10.1007/S002459900122.
```

```
@article{osti_21067542,
```

title = {A Dynamical Systems Analysis of Semidefinite Programming with Application to Quadratic Optimization with Pure Quadratic Equality Constraints},

author = {Orsi, R. J. and Mahony, R. E. and Moore, J. B.},

abstractNote = {This paper considers the problem of minimizing a quadratic cost subject to purely quadratic equality constraints. This problem is tackled by first relating it to a standard semidefinite programming problem. The approach taken leads to a dynamical systems analysis of semidefinite programming and the formulation of a gradient descent flow which can be used to solve semidefinite programming problems. Though the reformulation of the initial problem as a semidefinite pro- gramming problem does not in general lead directly to a solution of the original problem, the initial problem is solved by using a modified flow incorporating a penalty function.},

doi = {10.1007/S002459900122},

journal = {Applied Mathematics and Optimization},

issn = {0095-4616},

number = 2,

volume = 40,

place = {United States},

year = {1999},

month = {9}

}

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