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|Title:||Efficient optimization for L∞-problems using pseudoconvexity|
|Other Titles:||Efficient optimization for L infinity-problems using pseudoconvexity|
|Citation:||11th IEEE International Conference on Computer Vision, Rio de Janeiro, Brazil, October 14-20, 2007|
|Publisher Place:||United States|
|Conference Name:||IEEE International Conference on Computer Vision (11th : 2007 : Rio de Janeiro, Brazil)|
|Carl Olsson, Anders P. Eriksson and Fredrik Kahl|
|Abstract:||In this paper we consider the problem of solving geometric reconstruction problems with the L ∞-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 ∞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..|
|Appears in Collections:||Computer Science publications|
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