Minimizing Condition Number via Convex Programming
SIAM Journal on Matrix Analysis and Applications
Strong duality and minimal representations for cone optimization
Computational Optimization and Applications
Facial structure and representation of integer hulls of convex sets
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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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.