\relax \@writefile{toc}{\contentsline {section}{\numberline {1}Convex and differentiable}{1}} \@writefile{toc}{\contentsline {section}{\numberline {2}Constrained Optimization Examples}{2}} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Constrained optimization. Mary has a date with Cal; she wants to get there as soon as possible, but she has to stop by the river first. The optimal route can be seen as follows: all the routes of cost C (fixed) are ellipses centered in M and C; Mary should take consider the smallest ellipse \emph {tangent} to the river. Such an ellipse has the property that the tangent line (differential) in P for both the objective (route) and the constraint (river) have the same direction, there fore the two differentials are a proportional vectors. The proportionality constants are the Lagrangian Multipliers.}}{3}} \newlabel{constarined_optimization_1}{{1}{3}} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Constrained optimization}}{3}} \newlabel{constarined_optimization_2}{{2}{3}} \@writefile{toc}{\contentsline {section}{\numberline {3}Lagrangian multipliers}{3}} \@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces $f$ constrained by $g$}}{4}} \newlabel{lagrangian_example}{{3}{4}} \@writefile{toc}{\contentsline {section}{\numberline {4}Kuhn-Tucker Saddle point conditions}{5}} \@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Saddle}}{5}} \newlabel{saddle}{{4}{5}} \@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Saddle, linear $\alpha $}}{6}} \newlabel{saddle2}{{5}{6}} \@writefile{toc}{\contentsline {section}{\numberline {5}Karush-Kun-Tucker for differentiable, convex problems}{6}} \@writefile{toc}{\contentsline {section}{\numberline {6}The dual problem}{7}} \bibstyle{abbrv} \bibdata{../../bibtex/ir,../../bibtex/aslam,../../bibtex/query_local,../../bibtex/learning,../../bibtex/other,../../bibtex/math,bibtex/local,bibtex/1mq} \@writefile{toc}{\contentsline {section}{\numberline {7}Interior point methods}{8}}