Efficient Optimization for L-infinity Problems using Pseudoconvexity

Summary, in English

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: Carl Olsson; Anders P Eriksson; Fredrik Kahl
• Department/s: Mathematics (Faculty of Engineering)
• Publishing year: 2007
• Language: English
• Pages: 2025-2032
• Publication/Series: 2007 IEEE 11th International Conference on Computer Vision, vols 1-6
• Document type: Conference paper
• Topic: Mathematical Sciences
• Conference name: IEEE 11th International Conference on Computer Vision, 2007. ICCV 2007
• Conference date: 2007-10-14 - 2007-10-21
• Conference place: Rio de Janeiro, Brazil
• Status: Published
• ISBN/ISSN/Other: ISSN: 1550-5499