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Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.
8
votes
0
answers
207
views
Concavity of product and ratio of sums
Apologies if this question is not appropriate for MathOverflow. I have asked at Math.StackExchange without success.
Consider the function $f:\mathbb{R}^n\rightarrow \mathbb{R}$ defined as
$$
f(x)=\le …
6
votes
0
answers
254
views
Concavity of a function implicitly defined by a polynomial
Consider the following system of $n$ equations:
\begin{equation}f_j^2 = x_j^2\sum_{i=1}^n A_{ij} f_i
\tag{$\star$}
\end{equation}
where $A_{ij}\geq 0$ are known constants and where $x_j>0$ for all …
1
vote
1
answer
202
views
Does the value function of a quadratic program stay convex when adding constraints?
I am interested in the value function of a quadratic program of the form
$$
v(y)=\min_x \frac{1}{2} x^\top Q(y) x,
$$
subject to a linear equality constraint
$$
E(y)x=d(y),
$$
and a linear inequality …