  


On Sublinear Inequalities for Mixed Integer Conic Programs
Fatma KılınçKarzan (fkilincandrew.cmu.edu) Abstract: This paper studies $K$sublinear inequalities, a class of inequalities with strong relations to Kminimal inequalities for disjunctive conic sets. We establish a stronger result on the sufficiency of $K$sublinear inequalities. That is, we show that when $K$ is the nonnegative orthant or the secondorder cone, $K$sublinear inequalities together with the original conic constraint are always sufficient for the closed convex hull description of the associated disjunctive conic set. When $K$ is the nonnegative orthant, $K$sublinear inequalities are tightly connected to functions that generate cutsso called cutgenerating functions. In particular, we introduce the concept of relaxed cutgenerating functions and show that each $R^n_+$sublinear inequality is generated by one of these. We then relate the relaxed cutgenerating functions to the usual ones studied in the literature. Recently, under a structural assumption, Cornuejols, Wolsey and Yildiz established the sufficiency of cutgenerating functions in terms of generating all nontrivial valid inequalities of disjunctive sets where the underlying cone is nonnegative orthant. We provide an alternate and straightforward proof of this result under the same assumption as a consequence of the sufficiency of $R^n_+$sublinear inequalities and their connection with relaxed cutgenerating functions. Keywords: integer programming; disjunctive programming; conic programming; cutting planes Category 1: Integer Programming ((Mixed) Integer Linear Programming ) Citation: Download: [PDF] Entry Submitted: 07/10/2015 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  