solution to optimization problem

Question

For the problem: $\min {x_1}^2$ subject to $x_1 \leq -1$ and ${x_1}^2 + {x_2}^2 \leq 2$

The possible solutions are: $(x_1,x_2)= (-1,0)$ and $(x_1,x_2)= (-1,-1)$. The optimal value is $1$. Are these solutions correct? If yes, can I include both of them as optimal solution? I am new to optimization. Pls bear with me.

Your objective function does not depend on $x_2$, haven't you forgotten something? — , Jul 04 '17 at 12:42

score 0 · Answer 1 · answered Jul 04 '17 at 12:46

0

There are obviously more solutions: $x_1 = -1$ and $-1 \le x_2 \le 1$.

answered Jul 04 '17 at 12:46

So this problem has many optimal solutions but one optimal value ? – Jyothi Jain Jul 04 '17 at 13:21
Precisely, yes. – Jul 04 '17 at 13:53

solution to optimization problem

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