# Maximize a variable bounded by a convex hull

Consider the optimization problem: $$\max \theta$$

$$\text{s.t. }\theta\leq min\{A\alpha\}$$

$$\sum_{i=1}^{k} \alpha_i =1$$ $$\alpha_i\geq 0 \text{ for }\forall i$$

where $$\alpha=[\alpha_1,...,\alpha_k]^T$$ and $$A$$ is a $$L\times k$$ matrix with nonnegative entries. $$\min {A\alpha}$$ means the smallest entry of the vector $$A\alpha$$.

This problem should be solved by simplex method since it is a linear programming problem. But I was wondering if there is another easier approach for it. Thanks.

• What is $\min\{A\alpha\}$? the smallest entry of the vector $A\alpha$? – daw Oct 8 '19 at 10:06