# Tagged Questions

Convex Optimization is a special case of mathematical optimization. It includes Linear Programming and least-squares.

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### Showing the multivariate normal is log-concave?

I'm trying to show that $\log p(x) = -\frac{1}{2}(x-\mu)^{T} \Sigma^{-1}(x-\mu)$ is concave. How would I go about this in $\mathbb{R}^n$? I've tried taking derivatives but I'm getting stuck once I get ...
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### accomodating non-negativity constraint in the dual

Suppose the objective implicitly imposes non-negativity constraint, say, the objective is sum of square roots of the decision variables. Is it necessary to consider the inequality constraints imposing ...
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### Confusion related to explanation of convexity of a function

I was reading this paper where the define an optimization problem as where K and L are kernel matrices and $\pi$ is the permutation matrix. They have explained that the function is convex because ...
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Would anyone mind helping me solve this problem $$\min\space f(x) = \frac12 x^\mathrm TQx + bx + c \qquad \text{s.t. } \sum_i x_i=\lambda$$ where $x$ is a vector whose entries are positive ...
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