# Tagged Questions

Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

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### Is this function strongly convex? or could I find a value space to make this function strongly convex?

I want to judge if this function $f(x_1,x_2,...,x_n)=(\frac{x_1}{\sum_{i=1}^{n}{x_i}})^2+(\frac{x_2}{\sum_{i=1}^{n}{x_i}})^2+...+(\frac{x_n}{\sum_{i=1}^{n}{x_i}})^2$ strongly convex for each ...
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### Finding critical points and determining local maxima and minima for $f(x,y)=-x^3+4xy-2y^2+1$

Finding critical points and determining local maxima and minima for $f(x,y)=-x^3+4xy-2y^2+1$ First I took the following derivatives: $f_x=-3x^2+4y$ $f_{xx}=-6x$ $f_y=4x-4y$ $f_{yy}=-4$ ...
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### Weighted $L_1$ norm

I try minimizing the following expression : $V(x)=\sum_{i=1}^n|x_i - u|w_i$ $w_i > 0$ I need to find u that minimize this expression. I know how to do it for w=1 (which is is the median). ...
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Consider $x,y,z$ are $n$-dimensional variables, and $a,b,c$ are three nonnegative vectors. Let $f(x,y,z)=a^T x+b^T y+c^T z-\left(\|x\|_2^{2/3}+\|y\|_2^{2/3}+\|z\|_2^{2/3}\right)^3$. How to find the ...