%PDF-1.5
%
1 0 obj
<< /S /GoTo /D (section.1) >>
endobj
4 0 obj
(Introduction)
endobj
5 0 obj
<< /S /GoTo /D (subsection.1.1) >>
endobj
8 0 obj
(Outline)
endobj
9 0 obj
<< /S /GoTo /D (section.2) >>
endobj
12 0 obj
(Background)
endobj
13 0 obj
<< /S /GoTo /D (subsection.2.1) >>
endobj
16 0 obj
(Semidefinite programming)
endobj
17 0 obj
<< /S /GoTo /D (subsubsection.2.1.1) >>
endobj
20 0 obj
(Strict feasibility and facial reduction)
endobj
21 0 obj
<< /S /GoTo /D (subsection.2.2) >>
endobj
24 0 obj
(Group invariance and symmetry reduction, SR)
endobj
25 0 obj
<< /S /GoTo /D (subsubsection.2.2.1) >>
endobj
28 0 obj
(First symmetry reduction using X=B *\(x\))
endobj
29 0 obj
<< /S /GoTo /D (subsubsection.2.2.2) >>
endobj
32 0 obj
(Second symmetry reduction to block diagonal form using X=Q*\(x\)QT)
endobj
33 0 obj
<< /S /GoTo /D (section.3) >>
endobj
36 0 obj
(Facial reduction for the symmetry reduced program)
endobj
37 0 obj
<< /S /GoTo /D (subsection.3.1) >>
endobj
40 0 obj
(Rank preserving)
endobj
41 0 obj
<< /S /GoTo /D (subsection.3.2) >>
endobj
44 0 obj
(Exposing vectors)
endobj
45 0 obj
<< /S /GoTo /D (subsubsection.3.2.1) >>
endobj
48 0 obj
(Order of reductions)
endobj
49 0 obj
<< /S /GoTo /D (subsection.3.3) >>
endobj
52 0 obj
(Doubly nonnegative, DNN, program)
endobj
53 0 obj
<< /S /GoTo /D (subsubsection.3.3.1) >>
endobj
56 0 obj
(Facial reduction from the ground set for DNN)
endobj
57 0 obj
<< /S /GoTo /D (subsection.3.4) >>
endobj
60 0 obj
(Singularity degree)
endobj
61 0 obj
<< /S /GoTo /D (subsection.3.5) >>
endobj
64 0 obj
(Simplifications)
endobj
65 0 obj
<< /S /GoTo /D (section.4) >>
endobj
68 0 obj
(The alternating direction method of multipliers, ADMM)
endobj
69 0 obj
<< /S /GoTo /D (subsection.4.1) >>
endobj
72 0 obj
(Augmented Lagrangian)
endobj
73 0 obj
<< /S /GoTo /D (subsection.4.2) >>
endobj
76 0 obj
(On solving the -subproblem)
endobj
77 0 obj
<< /S /GoTo /D (subsection.4.3) >>
endobj
80 0 obj
(On solving the x-subproblem)
endobj
81 0 obj
<< /S /GoTo /D (section.5) >>
endobj
84 0 obj
(Numerical results)
endobj
85 0 obj
<< /S /GoTo /D (subsection.5.1) >>
endobj
88 0 obj
(The quadratic assignment problem, QAP)
endobj
89 0 obj
<< /S /GoTo /D (subsubsection.5.1.1) >>
endobj
92 0 obj
(Background for the QAP)
endobj
93 0 obj
<< /S /GoTo /D (subsubsection.5.1.2) >>
endobj
96 0 obj
(On solving QAPwith ADMM)
endobj
97 0 obj
<< /S /GoTo /D (subsubsection.5.1.3) >>
endobj
100 0 obj
(Numerical results for the QAP)
endobj
101 0 obj
<< /S /GoTo /D (subsection.5.2) >>
endobj
104 0 obj
(The graph partition problem \(GP\))
endobj
105 0 obj
<< /S /GoTo /D (subsubsection.5.2.1) >>
endobj
108 0 obj
(The general GP)
endobj
109 0 obj
<< /S /GoTo /D (subsubsection.5.2.2) >>
endobj
112 0 obj
(The vertex separator problem \(VSP\) and min-cut \(MC\) )
endobj
113 0 obj
<< /S /GoTo /D (section.6) >>
endobj
116 0 obj
(Conclusion)
endobj
117 0 obj
<< /S /GoTo /D (section*.4) >>
endobj
120 0 obj
(Bibliography)
endobj
121 0 obj
<< /S /GoTo /D (appendix.A) >>
endobj
124 0 obj
(red Response:to Associate Editor and Reviewers)
endobj
125 0 obj
<< /S /GoTo /D (subsubsection.A.0.1) >>
endobj
128 0 obj
(red Response:to Assoc. Editor)
endobj
129 0 obj
<< /S /GoTo /D (subsubsection.A.0.2) >>
endobj
132 0 obj
(red Response:on theoretical contributions)
endobj
133 0 obj
<< /S /GoTo /D (subsection.A.1) >>
endobj
136 0 obj
(Reviewer Report \043 1)
endobj
137 0 obj
<< /S /GoTo /D (subsubsection.A.1.1) >>
endobj
140 0 obj
(Major comments on the theory)
endobj
141 0 obj
<< /S /GoTo /D (subsubsection.A.1.2) >>
endobj
144 0 obj
( Major comments on the computation)
endobj
145 0 obj
<< /S /GoTo /D (subsubsection.A.1.3) >>
endobj
148 0 obj
(Minor comments)
endobj
149 0 obj
<< /S /GoTo /D (subsection.A.2) >>
endobj
152 0 obj
(Reviewer Report \043 2)
endobj
153 0 obj
<< /S /GoTo /D (subsubsection.A.2.1) >>
endobj
156 0 obj
(Major comments following preliminary comments)
endobj
157 0 obj
<< /S /GoTo /D (subsubsection.A.2.2) >>
endobj
160 0 obj
(Minor comments)
endobj
161 0 obj
<< /S /GoTo /D (subsection.A.3) >>
endobj
164 0 obj
(Reviewer Report \043 3)
endobj
165 0 obj
<< /S /GoTo /D [166 0 R /Fit] >>
endobj
189 0 obj
<<
/Length 2722
/Filter /FlateDecode
>>
stream
xYYs~#J;Jq"rd? p ,AQr9qlޥx/O{ON'cdhOXFyQ
{Xʼnm\uv%~j-ҿ~}iϻӈo_bHS]{xkH"Z}yEZDyk%E*!gu^:گ/^w処l}Kpؓ R22Jw=QƃN@(RZ;~D\"
ͫ˘iMR&D:e9|WV`*~]_ķ|n:]"HX1kw{t{XB ˣ4<C/i"b" VZ\=o&tlO&22DYЅPk*SW-|,orZ7pc&q 8B2T$P#&jݘ$RGJK
dWuDb7\^+Kxۘ7\A_q rY8{{]递&z@Lw {(vY7Bǯ+3'ݖo$beɨE痆ϟ!Y
bT msvLBpr-ˮ®@K%-*H!ѝ}]5"܉y
ہ/[Gq
/&
)xHHj tE[l^S?nNʢg5Z:lH7,XRHKD.pGt;Gz0qSҒw~
Tp&/_)=6eֶ6vBeֽ9KpT1v^Ve%;}Hgj[QBAD<9"=<ؾ̚sgPio&iB͜[~UËjY38@,%8a$*sYzd{bç ;HNgg;'){[߽8EǑ|m;fz2]"HDkv7'G~em[n*tT[\VՀM9HHCE6P;ZT Z~7v ]v^cX67aUŹ b3>ˎ
ECX,$E]8BX4wHjGvr
mcu0hV `q!vx:Q2p-ù ՞A;߮9
Fj~m%7NdHmpS6[MΛ*aY$Z@HtOg>z|ydA2XĆ3D|%dMOx6%sb&qQ pnHl8L%lWtffFОF:gH9SMP.rPZ%I7QV4m#Ngh$f3x)P:%tҊar
1ܱa˒:ᔣ>RNRZ;bjgB#5E"Aj9?ڥEUrNUH;@ Vzzp vVՂ:]Ya0LhއAa[>(73;jһӻb>A)SqtlJŦT).^q91i7Ŭ;T!=I!I,\J̒Zs%,b&?*·k:t8Jttuy.c]Zr':c/fhii1JPRQ)_W
YZš_HM8'K¤11W3f輴k a*3N$~Rd䎥#)6dh5$],mY }{~-˺/Cð& ;dMpO璛Ѵ#1wH7%$'SL7wĻ{dKGBM>
-!>{w+NvOaP܁ś /VIgh)u|OEkoCoW)fv,?Ԥ.olaQK6%u}c?s2zyu3oMѷ)fMQ2No9I]C;͛4:[2Z"0I]`?w7u)*ϋ{[O
~Wvt#J¿ KC:
endstream
endobj
166 0 obj
<<
/Type /Page
/Contents 189 0 R
/Resources 188 0 R
/MediaBox [0 0 612 792]
/Parent 207 0 R
/Annots [ 167 0 R 168 0 R 169 0 R 174 0 R 175 0 R 176 0 R 177 0 R 178 0 R 179 0 R 180 0 R 181 0 R 170 0 R 171 0 R 172 0 R 206 0 R 173 0 R ]
>>
endobj
167 0 obj
<<
/Type /Annot
/Border[0 0 1]/H/I/C[0 1 1]
/Rect [171.529 607.895 213.183 623.835]
/Subtype/Link/A<>
>>
endobj
168 0 obj
<<
/Type /Annot
/Border[0 0 1]/H/I/C[0 1 1]
/Rect [248.844 607.895 327.736 623.945]
/Subtype/Link/A<>
>>
endobj
169 0 obj
<<
/Type /Annot
/Border[0 0 1]/H/I/C[0 1 1]
/Rect [363.397 607.895 454.151 623.945]
/Subtype/Link/A<>
>>
endobj
174 0 obj
<<
/Type /Annot
/Subtype /Link
/Border[0 0 1]/H/I/C[1 0 0]
/Rect [83.244 306.059 170.766 315.627]
/A << /S /GoTo /D (section.1) >>
>>
endobj
175 0 obj
<<
/Type /Annot
/Subtype /Link
/Border[0 0 1]/H/I/C[1 0 0]
/Rect [99.607 292.509 162.448 302.078]
/A << /S /GoTo /D (subsection.1.1) >>
>>
endobj
176 0 obj
<<
/Type /Annot
/Subtype /Link
/Border[0 0 1]/H/I/C[1 0 0]
/Rect [83.244 265.93 167.092 277.619]
/A << /S /GoTo /D (section.2) >>
>>
endobj
177 0 obj
<<
/Type /Annot
/Subtype /Link
/Border[0 0 1]/H/I/C[1 0 0]
/Rect [99.607 252.381 252.206 264.07]
/A << /S /GoTo /D (subsection.2.1) >>
>>
endobj
178 0 obj
<<
/Type /Annot
/Subtype /Link
/Border[0 0 1]/H/I/C[1 0 0]
/Rect [124.698 238.831 336.267 250.521]
/A << /S /GoTo /D (subsubsection.2.1.1) >>
>>
endobj
179 0 obj
<<
/Type /Annot
/Subtype /Link
/Border[0 0 1]/H/I/C[1 0 0]
/Rect [99.607 225.282 352.418 236.972]
/A << /S /GoTo /D (subsection.2.2) >>
>>
endobj
180 0 obj
<<
/Type /Annot
/Subtype /Link
/Border[0 0 1]/H/I/C[1 0 0]
/Rect [124.698 211.127 367.655 224.029]
/A << /S /GoTo /D (subsubsection.2.2.1) >>
>>
endobj
181 0 obj
<<
/Type /Annot
/Subtype /Link
/Border[0 0 1]/H/I/C[1 0 0]
/Rect [124.698 197.578 513.417 212.341]
/A << /S /GoTo /D (subsubsection.2.2.2) >>
>>
endobj
170 0 obj
<<
/Type /Annot
/Border[0 0 1]/H/I/C[0 1 1]
/Rect [196.086 165.697 282.81 177.204]
/Subtype/Link/A<>
>>
endobj
171 0 obj
<<
/Type /Annot
/Border[0 0 1]/H/I/C[0 1 1]
/Rect [99.831 155.994 319.993 167.69]
/Subtype/Link/A<>
>>
endobj
172 0 obj
<<
/Type /Annot
/Border[0 0 1]/H/I/C[0 1 1]
/Rect [474.542 155.994 542.437 167.69]
/Subtype/Link/A<>
>>
endobj
206 0 obj
<<
/Type /Annot
/Border[0 0 1]/H/I/C[0 1 1]
/Rect [83.244 143.491 94.651 154.25]
/Subtype/Link/A<>
>>
endobj
173 0 obj
<<
/Type /Annot
/Border[0 0 1]/H/I/C[0 1 1]
/Rect [119.593 110.325 267.512 121.832]
/Subtype/Link/A<>
>>
endobj
190 0 obj
<<
/D [166 0 R /XYZ 83.24 721 null]
>>
endobj
191 0 obj
<<
/D [166 0 R /XYZ 84.24 720 null]
>>
endobj
200 0 obj
<<
/D [166 0 R /XYZ 84.24 349.446 null]
>>
endobj
188 0 obj
<<
/Font << /F16 192 0 R /F17 193 0 R /F24 194 0 R /F55 195 0 R /F8 196 0 R /F11 197 0 R /F14 198 0 R /F7 199 0 R /F67 201 0 R /F21 202 0 R /F25 203 0 R /F41 204 0 R /F54 205 0 R >>
/ProcSet [ /PDF /Text ]
>>
endobj
244 0 obj
<<
/Length 2017
/Filter /FlateDecode
>>
stream
xZKs۶Wpj&BxwNd㹛Zeě{@1Q%
|;/hǧWg?>""%8!M9Է-V+SwtݗuY,t5&W?\oI
$xS_[
|wI&S