Dear all

I am trying form the linear programming relation of this article(“Budget-Constrained Auctions with Heterogeneous Items”)'s LP2.

## It bring the constrains with the Myerson’s Lemma(Virtual Valuation).

link text

```
cvx_begin
variable X(Bidder,Item)
PartOfDemand=sum(Parameter_g.*X,2);
PartOfBudget=sum(((Parameter_g.*VirtualValuation).*X),2);
PartOfSold=sum(Parameter_g.*X,1);
maximize sum(sum((Parameter_g.*VirtualValuation).*X))
subject to
for i=1:Bidder
PartOfDemand(i) <=Demand(i)
end
for i=1:Bidder
PartOfBudget(i) <=Budget(i)
end
for j=1:Item
PartOfSold(j) <=1
end
for i=1:Bidder
for j=1:Item
0<= X(i,j) <=1
end
end
cvx_end
```

Is that a convex function ??