# Tag Info

1 vote

### If there's an optimal solution for a LP, does it have to be at one of the vertices?

Not exactly. The result you found says that if there is an optimal solution then there is an optimal solution at a corner. There could also be optimal solutions that occur at non-corners. For a ...
• 3,705

### Optimal basic feasible solution in which reduced cost vector has a negative component

It can easily be seen that $\bar{c} \in \mathbb R$ where $\mathbb R = \{\mathbb R_-,0,\mathbb R_+\}$. For any set $S \subset \mathbb N$ let define notation $c_S$ such that vector $c_S$ contains ...
• 142
1 vote

### demonstrating convexity of set defined by quadratic inequality

Consider the epigraph of $f$ which is the set {$(x,a):a\geq\,f(x)$} The function clearly has a minimum because $\bigtriangledown f(x)=0$ gives: $Ax+a=0$ and since $A$ is positive definite, hence ...
• 1,702