乗数法（拡張ラグランジュ関数法）のPython実装．
pip3 install numpy matplotlib jax
python3 example.py
initial point = [ 0.7701838 1.4904741 -0.5514398]
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iteration: 0 | objective: 1.504 | h_norm: 0.4029 | rho: 0.1
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iteration: 1 | objective: 1.225 | h_norm: 1.0567 | rho: 0.2
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iteration: 2 | objective: 1.085 | h_norm: 1.1801 | rho: 0.4
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iteration: 3 | objective: 0.903 | h_norm: 1.0766 | rho: 0.8
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iteration: 4 | objective: 0.593 | h_norm: 0.6171 | rho: 1.6
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iteration: 5 | objective: 0.355 | h_norm: 0.0901 | rho: 1.6
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iteration: 6 | objective: 0.350 | h_norm: 0.0880 | rho: 3.2
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iteration: 7 | objective: 0.374 | h_norm: 0.0328 | rho: 6.4
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iteration: 8 | objective: 0.388 | h_norm: 0.0115 | rho: 12.8
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iteration: 9 | objective: 0.398 | h_norm: 0.0020 | rho: 12.8
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iteration: 10 | objective: 0.399 | h_norm: 0.0036 | rho: 25.6
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iteration: 11 | objective: 0.396 | h_norm: 0.0008 | rho: 25.6
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iteration: 12 | objective: 0.395 | h_norm: 0.0001 | rho: 25.6
mulitiplier method is converged.
optimal point = [0.57314324 0.83327645 0.5695581 ], optimal value = 0.39528369903564453
elapsed time = 2.76 sec.
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今野浩, 山下浩: 非線形計画法, 日科技連
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Stephen Boyd and Lieven Vandenberghe: Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares