v2009.01.01 - Convex Optimization
v2009.01.01 - Convex Optimization v2009.01.01 - Convex Optimization
32 CHAPTER 1. OVERVIEW Figure 9: Three-dimensional reconstruction of David from distance data. Figure 10: Digital Michelangelo Project, Stanford University. Measuring distance to David by laser rangefinder. Spatial resolution is 0.29mm.
Chapter 2 Convex geometry Convexity has an immensely rich structure and numerous applications. On the other hand, almost every “convex” idea can be explained by a two-dimensional picture. −Alexander Barvinok [25, p.vii] As convex geometry and linear algebra are inextricably bonded, we provide much background material on linear algebra (especially in the appendices) although a reader is assumed comfortable with [287] [289] [176] or any other intermediate-level text. The essential references to convex analysis are [173] [266]. The reader is referred to [286] [25] [324] [37] [53] [263] [311] for a comprehensive treatment of convexity. There is relatively less published pertaining to matrix-valued convex functions. [186] [177,6.6] [255] 2001 Jon Dattorro. CO&EDG version 2009.01.01. All rights reserved. Citation: Jon Dattorro, Convex Optimization & Euclidean Distance Geometry, Meboo Publishing USA, 2005. 33
- Page 1 and 2: DATTORRO CONVEX OPTIMIZATION & EUCL
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- Page 5 and 6: for Jennie Columba ♦ Antonio ♦
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Chapter 2<br />
<strong>Convex</strong> geometry<br />
<strong>Convex</strong>ity has an immensely rich structure and numerous<br />
applications. On the other hand, almost every “convex” idea can<br />
be explained by a two-dimensional picture.<br />
−Alexander Barvinok [25, p.vii]<br />
As convex geometry and linear algebra are inextricably bonded, we provide<br />
much background material on linear algebra (especially in the appendices)<br />
although a reader is assumed comfortable with [287] [289] [176] or any other<br />
intermediate-level text. The essential references to convex analysis are [173]<br />
[266]. The reader is referred to [286] [25] [324] [37] [53] [263] [311] for a<br />
comprehensive treatment of convexity. There is relatively less published<br />
pertaining to matrix-valued convex functions. [186] [177,6.6] [255]<br />
2001 Jon Dattorro. CO&EDG version 2009.01.01. All rights reserved.<br />
Citation: Jon Dattorro, <strong>Convex</strong> <strong>Optimization</strong> & Euclidean Distance Geometry,<br />
Meboo Publishing USA, 2005.<br />
33
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