%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) 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 (Facial reduction and exposing vectors) endobj 45 0 obj << /S /GoTo /D (subsection.3.3) >> endobj 48 0 obj (Simplifications) endobj 49 0 obj << /S /GoTo /D (section.4) >> endobj 52 0 obj (The alternating direction method of multipliers, ADMM) endobj 53 0 obj << /S /GoTo /D (subsection.4.1) >> endobj 56 0 obj (Augmented Lagrangian) endobj 57 0 obj << /S /GoTo /D (subsection.4.2) >> endobj 60 0 obj (On solving the -subproblem) endobj 61 0 obj << /S /GoTo /D (subsection.4.3) >> endobj 64 0 obj (On solving the x-subproblem) endobj 65 0 obj << /S /GoTo /D (section.5) >> endobj 68 0 obj (Numerical results) endobj 69 0 obj << /S /GoTo /D (subsection.5.1) >> endobj 72 0 obj (The quadratic assignment problem \(QAP\)) endobj 73 0 obj << /S /GoTo /D (subsubsection.5.1.1) >> endobj 76 0 obj (Background for the QAP) endobj 77 0 obj << /S /GoTo /D (subsubsection.5.1.2) >> endobj 80 0 obj (On solving QAPwith ADMM) endobj 81 0 obj << /S /GoTo /D (subsubsection.5.1.3) >> endobj 84 0 obj (Numerical results for the QAP) endobj 85 0 obj << /S /GoTo /D (subsection.5.2) >> endobj 88 0 obj (The graph partition problem \(GP\)) endobj 89 0 obj << /S /GoTo /D (subsubsection.5.2.1) >> endobj 92 0 obj (The general GP) endobj 93 0 obj << /S /GoTo /D (subsubsection.5.2.2) >> endobj 96 0 obj (The vertex separator problem \(VSP\) and min-cut \(MC\) ) endobj 97 0 obj << /S /GoTo /D (section.6) >> endobj 100 0 obj (Conclusion) endobj 101 0 obj << /S /GoTo /D (section*.3) >> endobj 104 0 obj (Index) endobj 105 0 obj << /S /GoTo /D (section*.4) >> endobj 108 0 obj (Bibliography) endobj 109 0 obj << /S /GoTo /D [110 0 R /Fit] >> endobj 137 0 obj << /Length 2562 /Filter /FlateDecode >> stream xZ[s~ׯIj}ݵ+)bDd!=FؒSN ݧo\'.{~|1=1zF0#/56x~IZ@'٦[q?m՚UI[ծff/f*׀2o3WS]]ɶYv=fy3aAIl^$ѹ&By3Q4,5R2bz"zIO6a 7EVZ`0/V"8yqa8f|E[s LDfiWkf[zo֞a&! BA)a\ΛNI5S2y A ?K }GIq4imN|6K 2eM[4\փ*fӢ&ˋ9:X 'u''3E@fb50( # \V4k^&TjkEk4]-n\mKLgf5ȏ`יB9@+%Z[6;Jxke <,#4|y>l1H
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