(i) Let f: R? → R be defined as f(x1, x2) = -x3. Consider the minimization problem minen f(x), where N = {x E R² : |x2| 0}. %3D (a) Does the point 0 0 satisfy the first order necessary condition for a...

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(i) Let f: R? → R be defined as f(x1, x2) = -x3. Consider the minimization problem minen f(x),<br>where N = {x E R² : |x2| < xỉ and x1 > 0}.<br>%3D<br>(a) Does the point 0 0 satisfy the first order necessary condition for a local minimizer?<br>That is, is it true that dTVf(0, 0) > 0 for all feasible directions d at [0 0]'?<br>T<br>(b) Is the point 0 0] a local minimizer, strict local minimizer, local maximizer, strict<br>local maximizer, or none?<br>

Extracted text: (i) Let f: R? → R be defined as f(x1, x2) = -x3. Consider the minimization problem minen f(x), where N = {x E R² : |x2| < xỉ="" and="" x1=""> 0}. %3D (a) Does the point 0 0 satisfy the first order necessary condition for a local minimizer? That is, is it true that dTVf(0, 0) > 0 for all feasible directions d at [0 0]'? T (b) Is the point 0 0] a local minimizer, strict local minimizer, local maximizer, strict local maximizer, or none?

Jun 04, 2022

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(i) Let f: R? → R be defined as f(x1, x2) = -x3. Consider the minimization problem minen f(x), where N = {x E R² : |x2| 0}. %3D (a) Does the point 0 0 satisfy the first order necessary condition for a...

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