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Convex Optimization is a special case of mathematical optimization where the feasible region is convex and the objective is to either minimize a convex function or maximize a concave function.

21
votes
Probably you ask for a proof that the median solves the problem? Well, this can be done like this: The objective is piecewise linear and hence differentiable except for the points $m=x_i$. What is th …
answered Jan 16 '12 by Dirk
2
votes
Check Rockafellars "Convex Analysis" Theorem 32.2: If a convex function is defined on a set which is the convex hull of a set of points than the function attains its maximum at one of the points. If …
answered Dec 28 '14 by Dirk
1
vote
So you want to solve $$ \min_{\|p\|_1 \leq 1} f(q). $$ with $f(p)=(p-q)^TA(p-q)$. If $A$ is symmetic positive semidefinite this is a smooth convex objective with a convex constraint and hence, this ca …
answered Oct 27 '17 by Dirk
7
votes
Writing an optimization routine is like writing any other not too simple program and involves a fair amount of debugging. All things you mention in your question are good checks (i.e. taking care that …
answered Dec 4 '16 by Dirk