Iteration Algorithm for Computing Bounds in Quadratic Optimization Problems (1993)
| Venue: | Complexity in Numerical Optimization |
| Citations: | 7 - 0 self |
BibTeX
@INPROCEEDINGS{Kamath93iterationalgorithm,
author = {Anil P. Kamath and Narendra K. Karmarkar},
title = {Iteration Algorithm for Computing Bounds in Quadratic Optimization Problems},
booktitle = {Complexity in Numerical Optimization},
year = {1993},
pages = {254--268},
publisher = {World Scientific}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
We consider the problem of optimizing a quadratic function subject to integer constraints. This problem is NP-hard in the general case. We present a new polynomial time algorithm for computing bounds on the solutions to such optimization problems. We transform the problem into a problem for minimizing the trace of a matrix subject to positive definiteness condition. We then propose an interior-point method to solve this problem. We show that the algorithm takes no more than O(nL) iterations (where L is the the number of bits required to represent the input). The algorithm does two matrix inversions in each iteration . Keywords: Bounds, complexity, quadratic optimization, interior point methods. 1 Outline The second section of the paper shall introduce the problem of computing upper bounds on a quadratic optimization problem. We shall also motivate an interior point approach to solving the problem. The third section gives an interior point method for solving the problem. The algorith...
