Is there anyone who can give a hint for this Qn

Asked Dec 05 '20 at 14:16

Active Dec 05 '20 at 14:16

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$x^* \in R^3$

Maximize: $f(x)$ Subject to: $g_1(x) \le 1$ and $g_2(x) \le 3$

$g_1(x^*) = 1, g_2(x^*) = 2, ∇f(x^*) =4∇g_1(x^*)$ These are given

If first constraint change to $g_1(x) \le 0.99$, but second stays same. Approximately what is the maximum value of $f(x)$?

I tried to solve it by finding lambdas, but I couldn't. Therefore, Is there anyone who can help me?

asked Dec 05 '20 at 14:16

Jumbo09

1

hint: use the first order conditions of the Lagrangian – LinAlg Dec 05 '20 at 16:28
how do I find $\lambda_2$ ? because I ddon't know $∇g_2(x^*)$ – Jumbo09 Dec 05 '20 at 16:57
1

You can derive $\lambda_2$ from the information that is given. What is the stationarity condition of the unmodified problem? – LinAlg Dec 05 '20 at 17:05
@LinAlg: I thought that maximum value is 4.96, but I am not sure – Jumbo09 Dec 05 '20 at 17:06
you should provide some clarification for '4.96' – LinAlg Dec 05 '20 at 17:09

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