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Title: 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:
 [1];  [2];  [3]
  1. Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC 3052 (Australia)
  2. Heudiasyc - UTC UMR 6599, Centre de Recherche de Royallieu, BP 20529, 60205 Compiegne Cedex (France)
  3. 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}
}