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 3 Prove convexity of $f(x_1,x_2,x_3)=\frac{x_1^2+x_1+1}{x_2+x_3}$ over $\{(x_1,x_2,x_3) : x_2,x_3\gt0\}$ 3 Prove convexity of $f(x)=\sum_{i=1}^{n}{x_i\ln{x_i}}-\left(\sum_{i=1}^{n}{x_i}\right)\ln\left(\sum_{i=1}^{n}{x_i}\right)$ over $\mathbb{R}_{++}^n$ [duplicate] 1 Prove convexity of split function (linear and quadratic) 1 Gradient descent converges after $T \leq O(\log(1/\varepsilon))$ iterations for $f(x)=x^T A x$ where $A$ is positive definite matrix 1 Proving global minimum by lower bound of 2-variable function $f(x,y)=(x-2y)^4+64xy$

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 2 Prove convexity of split function (linear and quadratic) 0 Gradient descent converges after $T \leq O(\log(1/\varepsilon))$ iterations for $f(x)=x^T A x$ where $A$ is positive definite matrix

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 2 optimization × 9 0 logic × 3 2 convex-optimization × 8 0 maxima-minima × 3 2 convex-analysis × 4 0 functions × 3 2 calculus × 2 0 gradient-descent × 2 0 multivariable-calculus × 6 0 numerical-optimization × 2

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