Article ID: | iaor200954094 |
Country: | United States |
Volume: | 32 |
Issue: | 2 |
Start Page Number: | 395 |
End Page Number: | 412 |
Publication Date: | May 2007 |
Journal: | Mathematics of Operations Research |
Authors: | Pataki Gbor |
Keywords: | convex hulls |
When is the linear image of a closed convex cone closed? We present very simple and intuitive necessary conditions that (1) unify, and generalize seemingly disparate, classical sufficientconditions such as polyhedrality of the cone, and Slater–type conditions; (2) are necessary and sufficient, when the dual cone belongs to a class that we call nice cones (nice cones subsume all cones amenable to treatment by efficient optimization algorithms, for instance, polyhedral, semidefinite, and p–cones); and (3) provide similarly attractive conditions for an equivalent problem: the closedness of the sum of two closed convex cones.