This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=latex 2005.3.10) 10 JAN 2008 10:37 entering extended mode **seminar-00164-abstract-vrb.tex (./seminar-00164-abstract-vrb.tex LaTeX2e <2003/12/01> Babel and hyphenation patterns for american, french, german, ngerman, b ahasa, basque, bulgarian, catalan, croatian, czech, danish, dutch, esperanto, e stonian, finnish, greek, icelandic, irish, italian, latin, magyar, norsk, polis h, portuges, romanian, russian, serbian, slovak, slovene, spanish, swedish, tur kish, ukrainian, nohyphenation, loaded. (/usr/local/tex/te/3.0/texmf-dist/tex/latex/base/article.cls Document Class: article 2004/02/16 v1.4f Standard LaTeX document class (/usr/local/tex/te/3.0/texmf-dist/tex/latex/base/size10.clo File: size10.clo 2004/02/16 v1.4f Standard LaTeX file (size option) ) \c@part=\count79 \c@section=\count80 \c@subsection=\count81 \c@subsubsection=\count82 \c@paragraph=\count83 \c@subparagraph=\count84 \c@figure=\count85 \c@table=\count86 \abovecaptionskip=\skip41 \belowcaptionskip=\skip42 \bibindent=\dimen102 ) (./seminar-00164-abstract-vrb.aux) \openout1 = `seminar-00164-abstract-vrb.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 2. LaTeX Font Info: ... okay on input line 2. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 2. LaTeX Font Info: ... okay on input line 2. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 2. LaTeX Font Info: ... okay on input line 2. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 2. LaTeX Font Info: ... okay on input line 2. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 2. LaTeX Font Info: ... okay on input line 2. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 2. LaTeX Font Info: ... okay on input line 2. Overfull \hbox (85.49625pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 Many real-world applications, although being non-linear, ca n be well described by[] [] Overfull \hbox (85.49625pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 linearized models. Therefore, Linear Programming (LP) becam e a widely studied and[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 applied technique in many areas of science, industry and e conomy. Semidefinite[] [] Overfull \hbox (80.24629pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 Programming (SDP) is an extension of LP. A matrix-variable is optimized over the[] [] Overfull \hbox (80.24629pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 intersection of the cone of positive semidefinite matrices with an affine space.[] [] Overfull \hbox (85.49625pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 It turned out, that SDP can provide significantly stronger practical results than[] [] Overfull \hbox (80.24629pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 LP. Since then SDP turned out to be practical in a lot of different areas, like[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 combinatorial optimization, control theory, engineering, and more recently in[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 polynomial optimization. \\ Due to the numerous areas of a pplications, solving[] [] Overfull \hbox (85.49625pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 SDPs became a widely studied subject. Interior-Point Method s are the most popular[] [] Overfull \hbox (85.49625pt too wide) in paragraph at lines 21--21 []\OT1/cmtt/m/n/10 algorithms nowadays. Recently, bundle methods and applying a n augmented Lagrangian[] [] Overfull \hbox (85.49625pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 algorithm have been used for solving SDPs. \\ In this talk I will state the basic[] [] Overfull \hbox (80.24629pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 concept of SDP. I will show how to apply SDP to approximat e the max-cut problem[] [] Overfull \hbox (74.99634pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 and the coloring problem, two combinatorial optimization p roblems. Via the SDP[] [] Overfull \hbox (80.24629pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 relaxations of these two combinatorial optimization proble ms I will explain the[] [] Overfull \hbox (80.24629pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 methods for solving SDPs, in particular the recently develo ped bundle method for[] [] Overfull \hbox (64.49643pt too wide) in paragraph at lines 21--21 [] \OT1/cmtt/m/n/10 max-cut and the boundary point method to compute the Lo vasz theta-number.[] [] [1 ] (./seminar-00164-abstract-vrb.aux) ) Here is how much of TeX's memory you used: 203 strings out of 94500 2385 string characters out of 1173795 49348 words of memory out of 1000000 3456 multiletter control sequences out of 10000+50000 3808 words of font info for 15 fonts, out of 500000 for 2000 580 hyphenation exceptions out of 1000 23i,4n,17p,150b,130s stack positions out of 1500i,500n,5000p,200000b,5000s Output written on seminar-00164-abstract-vrb.dvi (1 page, 1772 bytes).