v2006.03.09 - Convex Optimization

Appendix FProof of EDM compositionF.1 EDM-entry exponential(4.10)D ∈ EDM n ⇔ [1 − e −λd ij] ∈ EDM n ∀λ > 0 (639)Lemma 2.1. from A Tour d’Horizon ...on Completion Problems. [145]The following assertions are equivalent: for D =[d ij , i,j =1... n] ∈ S n h andE n the elliptope in S n (4.9.1.0.1),(i) D ∈ EDM n(ii) e −λD ∆ = [e −λd ij] ∈ E n for all λ > 0(iii) 11 T − e −λD ∆ = [1 − e −λd ij] ∈ EDM n for all λ > 0⋄2001 Jon Dattorro. CO&EDG version 03.09.2006. All rights reserved.Citation: Jon Dattorro, Convex Optimization & Euclidean Distance Geometry,Meboo Publishing USA, 2005.585