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For questions about non-convex optimization problems where the objective or any of the constraints are non-convex.
5
votes
Convex vs Strictly Quasiconvex Functions in Optimization
My claim is that everything that can be formulated as a conic optimization problem using
Linear cones
Quadratic cones
Power cones
Exponential cones
Semi definite cone (with some qualifications)
ca …
15
votes
Accepted
Convexity of Variance Minimization
It holds
$$
\begin{array}{rcl}
\operatorname V(x) &= &\dfrac1N\left\| x-\dfrac{e^\top x}{N} e \right\|^2 \\
& = & \dfrac1N\left(x^\top x+\dfrac{(e^\top x)^2 e^\top e}{N^2}-2\dfrac{(e^\top x)^2}N\ …