{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "Solve the optimization problem:"
      ],
      "metadata": {
        "id": "p7SaYmMoMqBK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "fNpA94TAMsaZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "1. Plot the function level lines. Make some assumptions about the minimum of the function."
      ],
      "metadata": {
        "id": "NamhjdvYObIK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "2. Solve the problem numerically, using:\n",
        "    1. Heavy-Ball method (HB)\n",
        "    2. Nesterov's Accelerated Gradient Descent\n",
        "    3. Conjugate gradient method\n",
        "    4. Fletcher–Reeves Method\n",
        "\n",
        "It is necessary to implement the algorithms proposed in the lecture."
      ],
      "metadata": {
        "id": "vnLirxJsM5H9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "3. Illustrate the results obtained graphically."
      ],
      "metadata": {
        "id": "UhMF8WrzOzRi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "4. Compare the obtained results. Which method works better and why?"
      ],
      "metadata": {
        "id": "QUmhOyEjbFNu"
      }
    }
  ]
}