文档介绍：DATTORRO
CONVEX
OPTIMIZATION
&
EUCLIDEAN
DISTANCE
GEOMETRY
Mεβοο
Dattorro
CONVEX
OPTIMIZATION
&
EUCLIDEAN
DISTANCE
GEOMETRY
Meboo
Convex Optimization
&
Euclidean Distance Geometry
Jon Dattorro
εβoo Publishing
M
Meboo Publishing USA
PO Box 12
Palo Alto, California 94302
Dattorro, Convex Optimization & Euclidean Distance Geometry,
εβoo, 2005, .
M
ISBN 0976401304 (English) ISBN 9780615193687 (International II)
This is version : available in print, as conceived, in color.
cybersearch:
I. convex optimization
II. semidefinite program
III. rank constraint
IV. convex geometry
V. distance matrix
VI. convex cones
programs by Matlab
typesetting by
with donations from SIAM and AMS.
This searchable electronic color pdfBook is click-navigable within the text by
page, section, subsection, chapter, theorem, example, definition, cross reference,
citation, equation, figure, table, and hyperlink. A pdfBook has no electronic copy
protection and can be read and printed by puters. The publisher hereby
grants the right to reproduce this work in any format but limited to personal use.
© 2001-2009 Meboo
All rights reserved.
for Jennie Columba
♦
Antonio
♦
♦
& Sze Wan
EDM = S S⊥ S
h ∩ c −+
¡ ¢
Prelude
The constant demands of my department and university and the
ever increasing work needed to obtain funding have stolen much of
my precious thinking time, and I sometimes yearn for the halcyon
days of Bell Labs.
Steven Chu, Nobel laureate [77]
−
Convex Analysis is the calculus of inequalities while Convex Optimization is
its application. Analysis is inherently the domain of a mathematician while
Optimization belongs to the engineer. Practitioners in the art of Convex
Optimization engage themselves with discovery of which hard problems,
perhaps previously believed nonconvex, can be transformed into convex
equivalents; because once convex form of a problem is found, then a g