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"```jl\n",
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"```jl\n",
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"d²gdλ²(λ; r=0.5) = ForwardDiff.derivative(λ -> dgdλ(λ; r=0.5), λ)\n",
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"d²gdλ²(λ; r=0.5) = ForwardDiff.derivative(λ -> dgdλ(λ; r=0.5), λ)\n",
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"```\n",
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"```\n",
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"Use this to implement a Newton iteration to maximize $g(\\lambda)$ (for $$\\lambda \\ge 0$$) by finding a root of $g'(\\lambda)$, starting with an initial guess of $\\lambda=0$, for $r = 0.5$. (It should converge in only a few iterations. The solution should have $\\lambda > 0$ in this case because \_\_\_\_\_\_.) To at least 8 significant digits, give the resulting dual optimum $\\lambda_*$ and the primal optimum $x_*$ (strong duality holds in this convex problem!), and check that $x_*$ is feasible."
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"Use this to implement a Newton iteration to maximize $g(\\lambda)$ (for $\\lambda \\ge 0$) by finding a root of $g'(\\lambda)$, starting with an initial guess of $\\lambda=0$, for $r = 0.5$. (It should converge in only a few iterations. The solution should have $\\lambda > 0$ in this case because ...?) To at least 8 significant digits, give the resulting dual optimum $\\lambda_*$ and the primal optimum $x_*$ (strong duality holds in this convex problem!), and check that $x_*$ is feasible."
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]
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]
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},
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},
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{
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{
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