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.

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

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