v2009.01.01 - Convex Optimization
v2009.01.01 - Convex Optimization v2009.01.01 - Convex Optimization
480 CHAPTER 6. CONE OF DISTANCE MATRICES EDM 2 = S 2 h ∩ ( ) S 2⊥ c − S 2 + svec S 2⊥ c svec S 2 c svec ∂S 2 + svec S 2 h 0 Figure 124: Orthogonal complement S 2⊥ c (1876) (B.2) of geometric center subspace (a plane in isometrically isomorphic R 3 ; drawn is a tiled fragment) apparently supporting positive semidefinite cone. (Rounded vertex is artifact of plot.) Line svec S 2 c = aff cone T (1148) intersects svec ∂S 2 + , also drawn in Figure 122; it runs along PSD cone boundary. (confer Figure 105)
6.8. DUAL EDM CONE 481 EDM 2 = S 2 h ∩ ( ) S 2⊥ c − S 2 + svec S 2⊥ c svec S 2 c svec S 2 h 0 − svec ∂S 2 + Figure 125: EDM cone construction in isometrically isomorphic R 3 by adding polar PSD cone to svec S 2⊥ c . Difference svec ( S 2⊥ c − S+) 2 is halfspace partially bounded by svec S 2⊥ c . EDM cone is nonnegative halfline along svec S 2 h in this dimension.
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- Page 445 and 446: Chapter 6 Cone of distance matrices
- Page 447 and 448: 6.1. DEFINING EDM CONE 447 6.1 Defi
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- Page 493 and 494: 6.10. POSTSCRIPT 493 When D is an E
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- Page 501 and 502: 501 7.0.3 Problem approach Problems
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6.8. DUAL EDM CONE 481<br />
EDM 2 = S 2 h ∩ ( )<br />
S 2⊥<br />
c − S 2 +<br />
svec S 2⊥<br />
c<br />
svec S 2 c<br />
svec S 2 h<br />
0<br />
− svec ∂S 2 +<br />
Figure 125: EDM cone construction in isometrically isomorphic R 3 by adding<br />
polar PSD cone to svec S 2⊥<br />
c . Difference svec ( S 2⊥<br />
c − S+) 2 is halfspace partially<br />
bounded by svec S 2⊥<br />
c . EDM cone is nonnegative halfline along svec S 2 h in<br />
this dimension.
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