diff --git a/experiments/playground.ipynb b/experiments/playground.ipynb
deleted file mode 100644
index 4c4cdba3..00000000
--- a/experiments/playground.ipynb
+++ /dev/null
@@ -1,466 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "dict1 = {\"a\":1, \"b\":2}\n",
-    "dict2 = {\"a\":10, \"b\":20, \"c\":3, \"d\":4}"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import cvxpy as cp\n",
-    "import numpy as np"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "a = cp.Parameter(shape=1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "a.value = np.array([0])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "ValueError",
-     "evalue": "Invalid dimensions (2,) for Parameter value.",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
-      "Cell \u001b[0;32mIn[25], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43ma\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvalue\u001b[49m \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mzeros(\u001b[38;5;241m2\u001b[39m)\n",
-      "File \u001b[0;32m~/Documents/Stanford/Research/My papers/markowitz/code/cvxmarkowitz/.venv/lib/python3.9/site-packages/cvxpy/expressions/constants/parameter.py:87\u001b[0m, in \u001b[0;36mParameter.value\u001b[0;34m(self, val)\u001b[0m\n\u001b[1;32m     85\u001b[0m \u001b[39m@value\u001b[39m\u001b[39m.\u001b[39msetter\n\u001b[1;32m     86\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mvalue\u001b[39m(\u001b[39mself\u001b[39m, val):\n\u001b[0;32m---> 87\u001b[0m     \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_value \u001b[39m=\u001b[39m \u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49m_validate_value(val)\n",
-      "File \u001b[0;32m~/Documents/Stanford/Research/My papers/markowitz/code/cvxmarkowitz/.venv/lib/python3.9/site-packages/cvxpy/expressions/leaf.py:394\u001b[0m, in \u001b[0;36mLeaf._validate_value\u001b[0;34m(self, val)\u001b[0m\n\u001b[1;32m    392\u001b[0m val \u001b[39m=\u001b[39m intf\u001b[39m.\u001b[39mconvert(val)\n\u001b[1;32m    393\u001b[0m \u001b[39mif\u001b[39;00m intf\u001b[39m.\u001b[39mshape(val) \u001b[39m!=\u001b[39m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mshape:\n\u001b[0;32m--> 394\u001b[0m     \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\n\u001b[1;32m    395\u001b[0m         \u001b[39m\"\u001b[39m\u001b[39mInvalid dimensions \u001b[39m\u001b[39m%s\u001b[39;00m\u001b[39m for \u001b[39m\u001b[39m%s\u001b[39;00m\u001b[39m value.\u001b[39m\u001b[39m\"\u001b[39m \u001b[39m%\u001b[39m\n\u001b[1;32m    396\u001b[0m         (intf\u001b[39m.\u001b[39mshape(val), \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m\u001b[39m__class__\u001b[39m\u001b[39m.\u001b[39m\u001b[39m__name__\u001b[39m)\n\u001b[1;32m    397\u001b[0m     )\n\u001b[1;32m    398\u001b[0m projection \u001b[39m=\u001b[39m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mproject(val)\n\u001b[1;32m    399\u001b[0m \u001b[39m# ^ might be a numpy array, or sparse scipy matrix.\u001b[39;00m\n",
-      "\u001b[0;31mValueError\u001b[0m: Invalid dimensions (2,) for Parameter value."
-     ]
-    }
-   ],
-   "source": [
-    "a.value = np.zeros(2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "argument[1].is_incr(0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "4.0"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.array([1, 1]) @ np.array([[1.0, 0.5], [0.5, 2.0]]) @ np.array([1, 1])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1.1287249999999998"
-      ]
-     },
-     "execution_count": 55,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "0.7**2 + 0.75**2 + 0.1**2*(0.5**2 + 0.1**2 + 0.2**2) + (0.2*0.7+0.1*0.75)**2 + 0.3**2*(0.5**2 + 0.1**2 + 0.2**2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1.098725"
-      ]
-     },
-     "execution_count": 52,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "0.7**2 + 0.75**2 + (0.2*0.7+0.1*0.75)**2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1.128725"
-      ]
-     },
-     "execution_count": 57,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "1.098725+0.030000000000000006"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0.030000000000000006"
-      ]
-     },
-     "execution_count": 58,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "0.1**2*(0.5**2 + 0.1**2 + 0.2**2) + 0.3**2*(0.5**2 + 0.1**2 + 0.2**2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0.17320508075688776"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.sqrt(0.030000000000000006)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "1.1337249999999999"
-      ]
-     },
-     "execution_count": 54,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "0.035 + 1.098725"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[ 0.62640616],\n",
-       "       [ 0.37359384],\n",
-       "       [-2.86631143]])"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "Sigma = np.array([[2,0.4], [0.4, 3]])\n",
-    "d = np.array([0.15, 0.3])\n",
-    "\n",
-    "ones = np.ones(2).reshape(-1,1)\n",
-    "\n",
-    "A1 = np.hstack([2*(Sigma + np.outer(d,d)), ones])\n",
-    "A2 = np.hstack([ones.T, np.zeros((1,1))])\n",
-    "A = np.vstack([A1, A2])\n",
-    "\n",
-    "b = np.vstack([np.zeros((2,1)), np.ones((1,1))])\n",
-    "w_star = np.linalg.solve(A, b)\n",
-    "w_star"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1. , 0.5],\n",
-       "       [0.5, 2. ]])"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.array([[1.0, 0.5], [0.5, 2.0]])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "obj.is_dcp()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n",
-      "True\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "n = 10\n",
-    "L = cp.Parameter(\n",
-    "    shape=(n, n),\n",
-    "    name=\"chol\",\n",
-    "    value=np.zeros((n, n)),\n",
-    ")\n",
-    "w = cp.Variable(n)\n",
-    "\n",
-    "e = cp.Parameter(shape=n, value=np.zeros(n), nonneg=True)\n",
-    "\n",
-    "\n",
-    "argument = cp.hstack([L@w, cp.sum(w)])\n",
-    "obj = cp.norm2(argument)\n",
-    "\n",
-    "# obj = cp.norm2(L@w)\n",
-    "print(argument.is_affine())\n",
-    "for i in range(11):\n",
-    "    print(argument[i].is_convex())\n",
-    "    print(argument.is_incr(i))\n",
-    "    \n",
-    "\n",
-    "\n",
-    "# obj.is_convex()\n",
-    "\n",
-    "prob = cp.Problem(cp.Minimize(obj))\n",
-    "prob.is_dcp()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 99,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 99,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "a = cp.Parameter()\n",
-    "\n",
-    "w = cp.Variable()\n",
-    "\n",
-    "prob = cp.Problem(cp.Minimize(cp.square(a*w)))\n",
-    "\n",
-    "prob.is_dpp()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 91,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(11,)"
-      ]
-     },
-     "execution_count": 91,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "argument.shape"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 94,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(20,)"
-      ]
-     },
-     "execution_count": 94,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "np.random.uniform(size=20).shape"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3.9.12 ('.venv': poetry)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.9.12"
-  },
-  "orig_nbformat": 4,
-  "vscode": {
-   "interpreter": {
-    "hash": "61cc297eca37719bb19fab84c89bdabd630ebd76dfae75f14ab889350806e9ac"
-   }
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}