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Given real vectors $v$ and $r$ of the same size, what are the following?

1. $\inf\{v'R^{-1}v \colon R>0, \text{diag}(R)= r\}$
2. $\sup\{v'Rv \colon R>0, \text{diag}(R)= r\}$

Note: $R > 0$ denotes positive definiteness, $x'$ denotes transpose, $\text{diag}(R)$ is the vector of the diagonal entries of matrix $R$.

Given real vectors $v$ and $r$ of the same size, what are the following?

1. $\inf\{v'R^{-1}v ~ \colon ~ R>0 \, , \, \text{diag}(R)= r\}$
2. $\sup\{v'Rv ~ \colon ~ R>0\, , \, \text{diag}(R)= r\}$

Note: $R > 0$ denotes positive definiteness, $x'$ denotes transpose, $\text{diag}(R)$ is the vector of the diagonal entries of matrix $R$.

Given real vectors v and r of the same size, what are the following, and how are they duals?

1. inf{v'*inv(R)*v : R>0, diag(R)= r}
2. sup{v'Rv : R>0, diag(R)= r}

Note: R > 0 denotes positive definiteness, x' denotes transpose, and inf, and sup are the infimum and supremum.

Given real vectors $v$ and $r$ of the same size, what are the following?

1. $\inf\{v'R^{-1}v \colon R>0, \text{diag}(R)= r\}$
2. $\sup\{v'Rv \colon R>0, \text{diag}(R)= r\}$

Note: $R > 0$ denotes positive definiteness, $x'$ denotes transpose, $\text{diag}(R)$ is the vector of the diagonal entries of matrix $R$.

Given real vectors v and r of the same size, what are the following, and how are they duals?

1. inf{v'*inv(R)*v : R>0, diag(R)= r}
2. sup{v'Rv : R>0, diag(R)= r} Note: R > 0 denotes positive definiteness, x' denotes transpose, and inf, and sup are the infimum and supremum.

Given real vectors v and r of the same size, what are the following, and how are they duals?

1. inf{v'*inv(R)*v : R>0, diag(R)= r}
2. sup{v'Rv : R>0, diag(R)= r}

Note: R > 0 denotes positive definiteness, x' denotes transpose, and inf, and sup are the infimum and supremum.