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### Questions (16)

 6 Show that $\max$ function on $\mathbb R^n$ is convex 3 Prove the bounds of Log-Sum-Exp function 2 Prove this function is unbounded below 2 Why should we change variable for this optimization problem? 2 Derive dual problem for this optimization problem without using conjugate function

### Reputation (343)

 +10 Proving an inequality on matrix norm +10 Meaning of superscript (1) in “$v_1(M) = \arg\min_x \|M - xx^T\|_2, x^{(1)}\ge0$” +10 Prove this function is unbounded below +10 Derive dual problem for this optimization problem without using conjugate function

 0 Prove this function is unbounded below 0 Derive dual problem for this optimization problem without using conjugate function 0 The difference between affine set and affine hull

### Tags (19)

 0 convex-optimization × 8 0 linear-programming × 2 0 linear-algebra × 6 0 eigenvalues-eigenvectors × 2 0 convex-analysis × 5 0 lagrange-multiplier × 2 0 optimization × 4 0 analysis × 2 0 inequality × 2 0 matrices