convex set optimization problem

Question

If I have a convex set $ \min f(x) $

$\sum_{i=1}^n x_{i} =1$ where $x\geq 0$.

Will an $\overline x$ (a local minimizer), if $x_{i} >0$ be

$ \dfrac{\partial{f(x)}}{\partial{x_{i}}} \geq \dfrac{\partial{f(x})}{\partial{x_{j}}} $ for all $j$

1)why would that be so ?

2) Does it matter if $f: \Bbb{R}^{n} \to \Bbb{R}$ is continuously differntiable ?

score 0 · Answer 1 · answered Oct 04 '13 at 15:11

0

I assume you meant $$\frac{\partial f}{\partial x_i}(\bar{x}) \geq \frac{\partial f}{\partial x_j}(\bar{x})?$$

Notice that the constraints are symmetric in the unknowns. Without some more information about $f$, there is no reason an asymmetry must appear in the derivatives of $f$ at $\bar{x}$.

answered Oct 04 '13 at 15:11

user7530

49,280

How can i show that if \overline{x} is a local minimizer then if x_{i} > 0; \partial{f(x)}/\partial{x_{i}} \geq \partial{f(x)}/\partial{x_{j}} for all j – Viper Maverick Oct 07 '13 at 10:20
The f(x) is ∑ni=1xi=1 x≥0. – Viper Maverick Oct 07 '13 at 10:21

convex set optimization problem

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