Efficient Optimization for L-infinity Problems using Pseudoconvexity
(2007) IEEE 11th International Conference on Computer Vision, 2007. ICCV 2007 p.2025-2032- Abstract
- In this paper we consider the problem of solving geometric reconstruction problems with the L-infinity-norm. Previous work has shown that globally optimal solutions can be computed reliably for a series of such problems. The methods for computing the solutions have relied on the property of quasiconvexity. For quasiconvex problems, checking if there exists a solution below a certain objective value can be posed as a convex feasibility problem. To solve the L-infinity-problem one typically employs a bisection algorithm, generating a sequence of convex problems. In this paper we present more efficient ways of computing the solutions. We derive necessary and sufficient conditions for a global optimum. A key property is that of... (More)
- In this paper we consider the problem of solving geometric reconstruction problems with the L-infinity-norm. Previous work has shown that globally optimal solutions can be computed reliably for a series of such problems. The methods for computing the solutions have relied on the property of quasiconvexity. For quasiconvex problems, checking if there exists a solution below a certain objective value can be posed as a convex feasibility problem. To solve the L-infinity-problem one typically employs a bisection algorithm, generating a sequence of convex problems. In this paper we present more efficient ways of computing the solutions. We derive necessary and sufficient conditions for a global optimum. A key property is that of pseudoconvexity, which is a stronger condition than quasiconvexity. The results open up the possibility of using local optimization methods for more efficient computations. We present two such algorithms. The first one is an interior point method that uses the KKT conditions and the second one is similar to the bisection method in the sense it solves a sequence of SOCP problems. Results are presented and compared to the standard bisection algorithm on real data for various problems and scenarios with improved performance. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/787821
- author
- Olsson, Carl LU ; Eriksson, Anders P LU and Kahl, Fredrik LU
- organization
- publishing date
- 2007
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- 2007 IEEE 11th International Conference on Computer Vision, vols 1-6
- pages
- 2025 - 2032
- conference name
- IEEE 11th International Conference on Computer Vision, 2007. ICCV 2007
- conference location
- Rio de Janeiro, Brazil
- conference dates
- 2007-10-14 - 2007-10-21
- external identifiers
-
- wos:000255099302001
- ISSN
- 1550-5499
- language
- English
- LU publication?
- yes
- id
- adbccfda-1083-4f4b-9b2b-6b3ee1918530 (old id 787821)
- date added to LUP
- 2016-04-04 09:26:37
- date last changed
- 2025-04-04 14:39:56
@inproceedings{adbccfda-1083-4f4b-9b2b-6b3ee1918530,
abstract = {{In this paper we consider the problem of solving geometric reconstruction problems with the L-infinity-norm. Previous work has shown that globally optimal solutions can be computed reliably for a series of such problems. The methods for computing the solutions have relied on the property of quasiconvexity. For quasiconvex problems, checking if there exists a solution below a certain objective value can be posed as a convex feasibility problem. To solve the L-infinity-problem one typically employs a bisection algorithm, generating a sequence of convex problems. In this paper we present more efficient ways of computing the solutions. We derive necessary and sufficient conditions for a global optimum. A key property is that of pseudoconvexity, which is a stronger condition than quasiconvexity. The results open up the possibility of using local optimization methods for more efficient computations. We present two such algorithms. The first one is an interior point method that uses the KKT conditions and the second one is similar to the bisection method in the sense it solves a sequence of SOCP problems. Results are presented and compared to the standard bisection algorithm on real data for various problems and scenarios with improved performance.}},
author = {{Olsson, Carl and Eriksson, Anders P and Kahl, Fredrik}},
booktitle = {{2007 IEEE 11th International Conference on Computer Vision, vols 1-6}},
issn = {{1550-5499}},
language = {{eng}},
pages = {{2025--2032}},
title = {{Efficient Optimization for L-infinity Problems using Pseudoconvexity}},
year = {{2007}},
}