<jupyter_start><jupyter_text>W09-W2: Nonlinear optimisation--- Displaying solutionsSolutions will be released after the workshop, as a new `.txt` file in the same GitHub repository. After pulling the file to Noteable, **run the following cell** to create clickable buttons under each exercise, which will allow you to reveal the solutions.<jupyter_code>%run scripts/create_widgets.py W09-W2<jupyter_output><empty_output><jupyter_text>Part a) Study the [scipy.optimize.minimize](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html) documentation and do the examples.  Part b) Solve the following unconstrained maximisation problem$$\max_x \left(126x_1 - 9 x_1^2 + 182x_2 - 13 x_2^2\right)$$<jupyter_code>%run scripts/show_solutions.py W09-W2_partb<jupyter_output><empty_output><jupyter_text>Part c) Solve the following unconstrained maximisation problem$$\max_x \left(54x_1 - 9 x_1^2 + 78x_2 - 13 x_2^2\right)$$<jupyter_code>%run scripts/show_solutions.py W09-W2_partc<jupyter_output><empty_output><jupyter_text>Part d) Solve the following unconstrained minimisation problem$$\min_x \left(x_1^2 + x_1(1-x_2) + x_2^2 - x_2 x_3 + x_3^2 + x_3\right)$$<jupyter_code>%run scripts/show_solutions.py W09-W2_partd<jupyter_output><empty_output>
{'fraction_non_alphanumeric': 0.10996835443037975, 'fraction_numerical': 0.043512658227848104, 'mean_word_length': 6.666666666666667, 'pattern_counts': {'":': 0, '<': 17, '<?xml version=': 0, '>': 17, 'https://': 1, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'chain_length': '4', 'dir': 'jupyter-structured-clean-dedup', 'id': '184610', 'license': 'MIT', 'n_tokens_mistral': 490, 'n_tokens_neox': 455, 'n_words': 104, 'path': 'Workshops/W09-W2_NMfCE_Nonlinear_optimisation.ipynb', 'repo_name': 'DrFriedrich/nmfce-2021-22', 'size': '1264'}