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wsdewitt committed Apr 8, 2024
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"This is a special case of the generalized lasso.\n",
"Our penalized problem is\n",
"$$\n",
"\\min_{\\beta} f(\\beta) + \\lambda\\|D\\beta\\|_1,\n",
"\\min_{\\beta} f(\\beta) + \\lambda\\|\\mathfrak{D}\\beta\\|_1,\n",
"$$\n",
"where $f$ is the smooth piece of the objective.\n",
"To use FISTA, we'll need the gradient $\\nabla f$ and the proximal operator $\\mathrm{prox}_{\\lambda}$, defined as\n",
"$$\n",
"\\mathrm{prox}_{\\lambda}(x) = \\arg\\min_{y}\\frac{1}{2}\\|x - y\\|_2^2 + \\lambda\\|Dy\\|_1,\n",
"\\mathrm{prox}_{\\lambda}(x) = \\arg\\min_{y}\\frac{1}{2}\\|x - y\\|_2^2 + \\lambda\\|\\mathfrak{D}y\\|_1,\n",
"$$\n",
"which is equivalent to the constrained problem\n",
"$$\n",
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