# Tagged Questions

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### Constraint approximation in non-linear optimization

In given non-linear optimization problem \begin{equation*} \begin{aligned} & \underset{x \in\mathbb R^n}{\text{maximize}} & & f(x) = \alpha^2 \\ & \text{subject to} & c(p(x)) \le ...
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### Noncontinuous subadditive function

Is there any non-continuous additive function $f(x+y)= f(x)+f(y)$ from $\mathbb R$ to $\mathbb R$?
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### Minimization of $log_{a}(bc)+log_{b}(ac)+log_{c}(ab)$?

I am trying to find the minimal value of the expression: $log_{a}(bc)+log_{b}(ac)+log_{c}(ab)$ I think experience gives that the variables should be equal, if so then the minimal value is 6, but ...
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### Dimension analysis and explaining the $\varepsilon$

Reference of this post (page no 6 from equation 39) The time averaged total energy, $\bar E$, has the following $\varepsilon$ expansion in $D$ dimension: ...
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### The composition of two convex functions is convex

Let $f$ be a convex function on a convex domain $\Omega$ and $g$ a convex non-decreasing function on $\mathbb{R}$. prove that the composition of $g(f)$ is convex on $\Omega$. Under what conditions is ...
Let $\langle f_i \rangle _{i \in I}$ be a family of affine functions on a convex and compact set $\Omega \subset \mathbb{R^d}$ such that $f_i = a_i.x +b_i$ for $x \in \Omega$. Prove that f, defined by ...
Consider a locally-bounded, continuous, positive-semidefinite function $f: X \times Y \rightarrow \mathbb{R}_{\geq 0}$, where $X \subset \mathbb{R}^n$ is compact, $Y \subseteq \mathbb{R}^m$. For each ...