{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "**Start your solution by plotting the graph of the function and predicting where the function will have its minimum value.**"
      ],
      "metadata": {
        "id": "7-mGZXjZYLY_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "1. Implement **the heavy ball method** and apply it to solve the problem:\n",
        "![image.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "nstoq-Qx1VKP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "2. Implement **Nesterov’s Accelerated Gradient Descent** and apply it to solve the previous problem"
      ],
      "metadata": {
        "id": "JXMhDipRstjn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "3. Create graphs that show the results obtained (with a sequence of points)"
      ],
      "metadata": {
        "id": "43e9r8QAtF1t"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "4. Compare the results obtained"
      ],
      "metadata": {
        "id": "77kiFkfZgxix"
      }
    }
  ]
}