# Tag Info

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• 3,155

### Is the minization of a strictly convex function still strictly convex?

As demonstrated in the other answers, $g$ need not be strictly convex. However, under the additional assumption that the infimum is attained, i.e. $g(x) = \min_y f(x, y)$ for all $x$, one can show ...
• 90k
1 vote

• 12.7k

### Can someone give an example which satisfies the following conditions.

Examples are $$f(x) = x - \log(x+1)$$ or $$g(x) = x + e^{-x} - 1$$
• 12.5k

### Is the non-negative orthant a closed convex set?

The non-negative orthant can be defined by a conjunction of (strict) linear inequalities of the form ${\bf A} {\bf x} \leq {\bf b}$, where ${\bf A} = - {\bf I}$ and ${\bf b} = {\bf 0}$, and, thus, is ...
• 19.4k

• 28.3k