{"id":4778,"date":"2025-03-31T14:38:17","date_gmt":"2025-03-31T05:38:17","guid":{"rendered":"https:\/\/www.ktech.biz\/jp\/?p=4778"},"modified":"2025-05-26T11:54:49","modified_gmt":"2025-05-26T02:54:49","slug":"10-nlopt","status":"publish","type":"post","link":"https:\/\/www.ktech.biz\/jp\/tutorial\/10-nlopt\/","title":{"rendered":"10. \u975e\u7dda\u5f62\u6700\u9069\u5316 (\u591a\u5909\u6570)"},"content":{"rendered":"\n

10.1 \u6982\u8981<\/h3>\n

\u591a\u5909\u6570\u306e\u975e\u7dda\u5f62\u95a2\u6570 (\u4e00\u822c\u95a2\u6570) \u306e\u6700\u5c0f\u70b9 (\u7b26\u53f7\u3092\u9006\u306b\u3059\u308c\u3070\u6700\u5927\u70b9) \u3092\u6c42\u3081\u308b\u554f\u984c\u3092\u8003\u3048\u307e\u3059.
\n\\[
\nmin f(x_1, x_2, \\dots, x_n)
\n\\]\n\\(x_1, x_2, \\dots, x_n\\) \u3092\u8981\u7d20\u3068\u3059\u308b\u5217\u30d9\u30af\u30c8\u30eb\u3092 \\(\\boldsymbol{x}\\) \u3068\u8868\u3059\u3053\u3068\u306b\u3059\u308c\u3070, \u6b21\u306e\u3088\u3046\u306b\u30d9\u30af\u30c8\u30eb\u8868\u73fe\u3067\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059.
\n\\[
\nmin f(\\boldsymbol{x})
\n\\]\n1 \u5909\u6570\u306e\u5834\u5408\u3068\u540c\u69d8\u306b, \u5bfe\u8c61\u3068\u3059\u308b\u9818\u57df\u5185\u3067\u306f 1 \u3064\u306e\u6700\u5c0f\u70b9\u3057\u304b\u6301\u305f\u306a\u3044\u3082\u306e\u3068\u3057\u307e\u3059. \u3059\u306a\u308f\u3061, \u76ee\u7684\u3068\u3059\u308b\u6700\u5c0f\u70b9\u306e\u8fd1\u508d\u3060\u3051\u306b\u7740\u76ee\u3059\u308b\u3053\u3068\u306b\u3057\u307e\u3059. \u3053\u308c\u3092\u5c40\u6240\u7684\u6700\u9069\u5316\u3042\u308b\u3044\u306f\u5c40\u6240\u7684\u6700\u5c0f\u70b9\u3092\u6c42\u3081\u308b\u306a\u3069\u3068\u3044\u3044\u307e\u3059.<\/p>\n

10.2 \u591a\u5909\u6570\u95a2\u6570\u975e\u7dda\u5f62\u6700\u9069\u5316\u554f\u984c\u306e\u89e3\u6cd5<\/h3>\n

10.2.1 \u964d\u4e0b\u6cd5<\/h4>\n

\u6b21\u306e\u3088\u3046\u306a\u53cd\u5fa9\u3092\u884c\u3063\u3066\u6700\u5c0f\u70b9\u3092\u898b\u3064\u3051\u308b\u65b9\u6cd5\u3092\u964d\u4e0b\u6cd5\u3068\u3044\u3044\u307e\u3059.
\n\\[
\n\\boldsymbol{x_{k+1}} = \\boldsymbol{x_k} + \\alpha_k\\boldsymbol{d_k}
\n\\]\n\u3053\u3053\u3067, \\(\\boldsymbol{d_k}\\) \u3092\u65b9\u5411\u30d9\u30af\u30c8\u30eb, \\(\\alpha_k\\) \u3092\u30b9\u30c6\u30c3\u30d7\u9577\u3068\u3044\u3044\u307e\u3059.<\/p>\n

\u3053\u306e\u53cd\u5fa9\u3092\u56f3\u3067\u8868\u3059\u3068, \u307e\u305a\u73fe\u5728\u306e\u8fd1\u4f3c\u70b9\u304b\u3089\u6700\u5c0f\u70b9\u304c\u3042\u308b\u3068\u601d\u308f\u308c\u308b\u65b9\u5411\u306b\u5411\u3044\u305f\u65b9\u5411\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{d_k}\\) \u3092\u6c7a\u3081, \u6b21\u306b\u65b9\u5411\u30d9\u30af\u30c8\u30eb\u4e0a\u306e\u6700\u5c0f\u70b9\u3092\u6c42\u3081\u3066(1 \u5909\u6570\u306e\u6700\u9069\u5316\u3092\u884c\u3063\u3066)\u30b9\u30c6\u30c3\u30d7\u9577 \\(\\alpha_k\\) \u3092\u6c7a\u3081\u307e\u3059. \u3053\u306e\u3088\u3046\u306b\u3057\u3066\u6b21\u3005\u306b\u3088\u308a\u6700\u5c0f\u70b9\u306b\u8fd1\u3044\u8fd1\u4f3c\u70b9\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3059.<\/p>\n

\"\"<\/p>\n

10.2.1.1 \u6700\u6025\u964d\u4e0b\u6cd5<\/h4>\n

\u65b9\u5411\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066\u6700\u5927\u52fe\u914d\u65b9\u5411\u3092\u3068\u308b\u65b9\u6cd5\u3092\u6700\u6025\u964d\u4e0b\u6cd5\u3068\u3044\u3044\u307e\u3059. \u7b49\u9ad8\u7dda\u304c\u4f8b\u3048\u3070\u5186\u5f62\u306b\u8fd1\u3051\u308c\u3070\u3059\u3050\u306b\u6700\u5c0f\u70b9\u306b\u8fd1\u3065\u3044\u3066\u3044\u304d\u307e\u3059\u304c, \u5b9f\u969b\u306e\u554f\u984c\u3067\u306f\u610f\u5916\u3068\u53ce\u675f\u306f\u901f\u304f\u3042\u308a\u307e\u305b\u3093.<\/p>\n

10.2.1.2 \u30cb\u30e5\u30fc\u30c8\u30f3\u6cd5<\/h4>\n

\u95a2\u6570 \\(f\\) \u304c\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308b\u3068\u304d
\n\\[
\n\\nabla f(\\boldsymbol{x}) =
\n\\begin{pmatrix}
\n{\\partial}f(\\boldsymbol{x})\/{\\partial}x_1 \\\\
\n{\\partial}f(\\boldsymbol{x})\/{\\partial}x_2 \\\\
\n\\vdots \\\\
\n{\\partial}f(\\boldsymbol{x})\/{\\partial}x_n \\\\
\n\\end{pmatrix}
\n\\]\n\u3092 \\(f\\) \u306e\u52fe\u914d\u3068\u547c\u3073\u307e\u3059.<\/p>\n

\u3055\u3089\u306b, \\(f\\) \u304c 2 \u968e\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308b\u3068\u304d
\n\\[
\n\\boldsymbol{H}(\\boldsymbol{x}) =
\n\\begin{pmatrix}
\n{\\partial}^2f(\\boldsymbol{x})\/{{\\partial}x_1{\\partial}x_1} & {\\partial}^2f(\\boldsymbol{x})\/{{\\partial}x_2{\\partial}x_1} & \\cdots & {\\partial}^2f(\\boldsymbol{x})\/{{\\partial}x_n{\\partial}x_1} \\\\
\n{\\partial}^2f(\\boldsymbol{x})\/{{\\partial}x_1{\\partial}x_2} & {\\partial}^2f(\\boldsymbol{x})\/{{\\partial}x_2{\\partial}x_2} & \\cdots & {\\partial}^2f(\\boldsymbol{x})\/{{\\partial}x_n{\\partial}x_2} \\\\
\n\\vdots & \\vdots & \\ddots & \\vdots \\\\
\n{\\partial}^2f(\\boldsymbol{x})\/{{\\partial}x_1{\\partial}x_n} & {\\partial}^2f(\\boldsymbol{x})\/{{\\partial}x_2{\\partial}x_n} & \\cdots & {\\partial}^2f(\\boldsymbol{x})\/{{\\partial}x_n{\\partial}x_n} \\\\
\n\\end{pmatrix}
\n\\]\n\u3092 \\(f\\) \u306e\u30d8\u30c3\u30bb\u884c\u5217\u3068\u3044\u3044\u307e\u3059. \\(f\\) \u306e 1 \u968e\u3068 2 \u968e\u306e\u5c0e\u95a2\u6570\u304c\u9023\u7d9a\u3067\u3042\u308c\u3070 \\(\\boldsymbol{H}(\\boldsymbol{x})\\) \u306f\u6b63\u5b9a\u5024\u5bfe\u79f0\u884c\u5217\u306b\u306a\u308a\u307e\u3059.<\/p>\n

\u5c40\u6240\u7684\u6700\u5c0f\u70b9\u3092\u6c42\u3081\u308b\u305f\u3081\u306b\u65b9\u7a0b\u5f0f \\(\\nabla f(\\boldsymbol{x}) = 0\\) \u3092\u591a\u5909\u6570\u975e\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306e\u8981\u9818\u3067\u30cb\u30e5\u30fc\u30c8\u30f3\u6cd5\u3067\u89e3\u304f\u3053\u3068\u306b\u3059\u308b\u3068, \u53cd\u5fa9\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059.
\n\\[
\n\\begin{align}
\n& \\boldsymbol{d_k} = -\\boldsymbol{H}(\\boldsymbol{x_k})^{-1}\\nabla f(\\boldsymbol{x_k}) \\\\
\n& \\boldsymbol{x_{k+1}} = \\boldsymbol{x_k} + \\boldsymbol{d_k} \\\\
\n\\end{align}
\n\\]\n\\(\\boldsymbol{d_k}\\) \u306f\u964d\u4e0b\u6cd5\u306e\u65b9\u5411\u30d9\u30af\u30c8\u30eb\u306b\u306a\u308a, \u30cb\u30e5\u30fc\u30c8\u30f3\u65b9\u5411\u3068\u547c\u3070\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059. \u30b9\u30c6\u30c3\u30d7\u9577 \\(\\alpha_k\\) \u306f\u30cb\u30e5\u30fc\u30c8\u30f3\u6cd5\u306e\u5f0f\u3067\u306f 1 \u306b\u306a\u308a\u307e\u3059\u304c, \u5b9f\u969b\u306e\u554f\u984c\u3067\u306f\u30cb\u30e5\u30fc\u30c8\u30f3\u65b9\u5411\u4e0a\u3067 1 \u5909\u6570\u306e\u6700\u9069\u5316\u3092\u884c\u3063\u3066\u5b9a\u3081\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059.<\/p>\n

\u30cb\u30e5\u30fc\u30c8\u30f3\u6cd5\u306f, \u30d8\u30c3\u30bb\u884c\u5217\u3092\u8a08\u7b97\u3059\u308b\u306e\u304c\u9762\u5012\u306a\u3053\u3068, \u53cd\u5fa9\u306e\u9014\u4e2d\u3067\u30d8\u30c3\u30bb\u884c\u5217\u304c\u6b63\u5b9a\u5024\u3067\u306a\u304f\u306a\u308b\u3053\u3068\u304c\u3042\u308b\u306a\u3069\u306b\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059.<\/p>\n

10.2.1.3 \u6e96\u30cb\u30e5\u30fc\u30c8\u30f3\u6cd5<\/h4>\n

\u30cb\u30e5\u30fc\u30c8\u30f3\u6cd5\u306e\u554f\u984c\u70b9\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u30d8\u30c3\u30bb\u884c\u5217 \\(\\boldsymbol{H}(\\boldsymbol{x})\\) \u3092\u9069\u5f53\u306a\u6b63\u5b9a\u5024\u884c\u5217 \\(\\boldsymbol{H}\\) \u3067\u8fd1\u4f3c\u3059\u308b\u65b9\u6cd5\u3067\u3059.<\/p>\n

\u4ee3\u8868\u7684\u306a\u3082\u306e\u3068\u3057\u3066\u6b21\u306e BFGS (Broyden, Fletcher, Goldfarb, Shanno) \u516c\u5f0f\u304c\u3042\u308a\u307e\u3059.
\n\\[
\n\\boldsymbol{H_{k+1}} = \\boldsymbol{H_k} – \\boldsymbol{H_k}\\boldsymbol{s_k}(\\boldsymbol{H_k}\\boldsymbol{s_k})^T\/(\\boldsymbol{s_k}^T\\boldsymbol{H_k}\\boldsymbol{s_k}) + \\boldsymbol{y_k}\\boldsymbol{y_k}^T\/(\\boldsymbol{s_k}\\boldsymbol{y_k})
\n\\]\n\u3053\u3053\u3067, \\(\\boldsymbol{s_k} = \\boldsymbol{x_{k+1}} – \\boldsymbol{x_k}\\), \\(\\boldsymbol{y_k} = \\nabla f(\\boldsymbol{x_{k+1}}) – \\nabla f(\\boldsymbol{x_k})\\) \u3092\u8868\u3057\u307e\u3059.<\/p>\n

\\(\\boldsymbol{H_0}\\) \u3068\u3057\u3066\u306f\u9069\u5f53\u306a\u6b63\u5b9a\u5024\u5bfe\u79f0\u884c\u5217, \u4f8b\u3048\u3070\u5358\u4f4d\u884c\u5217\u3092\u3068\u308a, \u4ee5\u4e0b\u3053\u306e\u6f38\u5316\u5f0f\u3092\u9069\u7528\u3057\u307e\u3059.<\/p>\n

10.2.2 \u4fe1\u983c\u9818\u57df\u6cd5<\/h4>\n

\\(\\boldsymbol{x_k}\\) \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84 \\(\\delta_k\\) \u306e\u5186\u3092\u4fe1\u983c\u9818\u57df\u3068\u547c\u3076\u3053\u3068\u306b\u3057\u307e\u3059.<\/p>\n

\\(f\\) \u3092 \\(\\boldsymbol{x_k}\\) \u306e\u307e\u308f\u308a\u3067\u30c6\u30a4\u30e9\u30fc\u5c55\u958b\u3057, 2 \u6b21\u307e\u3067\u306e\u9805\u3092\u63a1\u7528\u3057\u3066\u8fd1\u4f3c\u95a2\u6570 \\(\\boldsymbol{q_k}(\\boldsymbol{s})\\) \u3092\u4f5c\u308a\u307e\u3059.
\n\\[
\n\\boldsymbol{q_k}(\\boldsymbol{s}) = f(\\boldsymbol{x_k}) + \\boldsymbol{s}^T \\nabla f(\\boldsymbol{x_k}) + (1\/2)\\boldsymbol{s}^T\\boldsymbol{H_k}\\boldsymbol{s}
\n\\]\n\u3053\u3053\u3067, \\(\\boldsymbol{H_k}\\) \u306f \\(\\boldsymbol{x_k}\\) \u306b\u304a\u3051\u308b \\(f\\) \u306e\u30d8\u30c3\u30bb\u884c\u5217\u307e\u305f\u306f\u6e96\u30cb\u30e5\u30fc\u30c8\u30f3\u6cd5\u306e\u3088\u3046\u306a\u8fd1\u4f3c\u884c\u5217\u3068\u3057\u307e\u3059.<\/p>\n

\u534a\u5f84 \\(\\delta_k\\) \u306e\u4fe1\u983c\u9818\u57df\u306f\u3053\u306e 2 \u6b21\u8fd1\u4f3c\u304c\u304a\u304a\u3080\u306d\u59a5\u5f53\u3068\u601d\u308f\u308c\u308b\u7bc4\u56f2\u3092\u8868\u3059\u3082\u306e\u3067\u3059.<\/p>\n

\u4fe1\u983c\u9818\u57df\u6cd5\u3067\u306f, \u9818\u57df\u5185\u3067\u8fd1\u4f3c\u95a2\u6570 \\(\\boldsymbol{q_k}(\\boldsymbol{s})\\) \u306e\u6700\u5c0f\u70b9 \\(\\boldsymbol{s_k}\\) \u3092\u6c42\u3081, \u305d\u308c\u3092\u5143\u306e\u554f\u984c\u306e\u6b21\u306e\u70b9 \\(\\boldsymbol{x_{k+1}}\\) \u3068\u3057\u3066\u53cd\u5fa9\u3057\u307e\u3059. \u3059\u306a\u308f\u3061, \u50be\u659c\u6cd5\u306b\u304a\u3051\u308b\u65b9\u5411\u30d9\u30af\u30c8\u30eb\u3068\u30b9\u30c6\u30c3\u30d7\u9577\u3092\u4e00\u5ea6\u306b\u6c7a\u3081\u3066\u3057\u307e\u3044\u307e\u3059.<\/p>\n

\\(\\boldsymbol{H_k}\\) \u304c\u6b63\u5b9a\u5024\u5bfe\u79f0\u3067 \\(||\\boldsymbol{H_k}^{-1}\\nabla f(\\boldsymbol{x_k})|| \\leq \\delta_k\\) \u3067\u3042\u308c\u3070, \u4fe1\u983c\u9818\u57df\u5185\u3067 \\(\\boldsymbol{s_k} = \\boldsymbol{H_k}^{-1}\\nabla f(\\boldsymbol{x_k})\\) \u3068\u306a\u308a\u307e\u3059. \u305d\u3046\u3067\u306a\u3051\u308c\u3070 \\(\\boldsymbol{s_k}\\) \u306f\u4fe1\u983c\u9818\u57df\u5916\u306b\u3042\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u306e\u3067, \u4fe1\u983c\u9818\u57df\u306e\u5186\u5468\u4e0a\u3067\u6700\u5c0f\u3068\u306a\u308b\u70b9\u3092\u63a2\u3057\u3066 \\(\\boldsymbol{s_k}\\) \u3068\u3057\u307e\u3059.<\/p>\n

\u5b9f\u969b\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u306f\u53ce\u675f\u72b6\u6cc1\u306b\u5fdc\u3058\u3066\u4fe1\u983c\u9818\u57df\u306e\u534a\u5f84 \\(\\delta_k\\) \u3092\u62e1\u5927\u30fb\u7e2e\u5c0f\u3059\u308b\u5236\u5fa1\u3082\u884c\u3044\u307e\u3059.<\/p>\n

10.3 XLPack \u3092\u4f7f\u3063\u305f\u591a\u5909\u6570\u95a2\u6570\u975e\u7dda\u5f62\u6700\u9069\u5316\u554f\u984c\u306e\u89e3\u304d\u65b9<\/h3>\n

\u975e\u7dda\u5f62\u6700\u9069\u5316\u554f\u984c\u306b\u306f, \u6e96\u30cb\u30e5\u30fc\u30c8\u30f3\u6cd5\u306e VBA \u30b5\u30d6\u30eb\u30fc\u30c1\u30f3 Optif0<\/strong> \u3092\u4f7f\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059. \u3053\u308c\u306f\u5fae\u5206 (\u52fe\u914d\u3068\u30d8\u30c3\u30bb\u884c\u5217) \u3092\u305d\u308c\u305e\u308c\u6709\u9650\u5dee\u5206\u8fd1\u4f3c\u3068BFGS\u516c\u5f0f\u3067\u8a08\u7b97\u3057\u30e6\u30fc\u30b6\u30fc\u306b\u3088\u308b\u5fae\u5206\u8a08\u7b97\u3092\u4e0d\u8981\u306b\u3057\u305f\u30b5\u30d6\u30eb\u30fc\u30c1\u30f3\u3067\u3059. Optif0 \u306f XLPack \u30bd\u30eb\u30d0\u30fc\u304b\u3089\u4f7f\u3046\u3053\u3068\u3082\u3067\u304d\u307e\u3059.<\/p>\n

\u6c42\u3081\u3089\u308c\u308b\u89e3\u306f\u5c40\u6240\u7684\u6700\u5c0f\u70b9\u3067\u3042\u308a, \u4e00\u822c\u306b\u5927\u57df\u7684\u6700\u5c0f\u70b9\u3092\u6c42\u3081\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093. \u5c40\u6240\u7684\u6700\u5c0f\u70b9\u306f\u3044\u304f\u3064\u3082\u5b58\u5728\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a, \u6c42\u3081\u305f\u3044\u6700\u5c0f\u70b9\u306b\u8fd1\u3044\u521d\u671f\u5024\u3092\u4e0e\u3048\u306a\u3044\u3068\u5225\u306e\u6700\u5c0f\u70b9\u306b\u53ce\u675f\u3059\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059.<\/p>\n

\u4f8b\u984c<\/h5>\n

\u6b21\u306e\u95a2\u6570\u306e\u6700\u5c0f\u70b9\u3092\u6c42\u3081\u308b.
\n\\[
\nf(x_1, x_2) = 100(x_2 – x_1^2)^2 + (1 – x_1)^2
\n\\]\n\u95a2\u6570\u306e\u5f62\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059 (\u7e26\u8ef8\u306f\u5bfe\u6570\u5024\u3067\u8868\u3057\u3066\u3044\u307e\u3059).<\/p>\n

\"\"<\/p>\n

\u3053\u306e\u95a2\u6570\u306f, \u30ed\u30fc\u30bc\u30f3\u30d6\u30ed\u30c3\u30af\u306e\u95a2\u6570\u3068\u547c\u3070\u308c, (-1.2, 1) \u3092\u51fa\u767a\u70b9\u3068\u3057\u3066, \u6700\u5c0f\u70b9 (1, 1) \u3092\u6c42\u3081\u308b\u30c6\u30b9\u30c8\u554f\u984c\u3068\u3057\u3066\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059 (\u306a\u308b\u3079\u304f\u8fd1\u3044\u521d\u671f\u5024\u3092\u4e0e\u3048\u308b\u3068\u3044\u3046\u539f\u5247\u306b\u306f\u6cbf\u3044\u307e\u305b\u3093\u304c\u30c6\u30b9\u30c8\u7528\u3068\u3057\u3066\u3042\u3048\u3066\u9060\u304f\u306e\u521d\u671f\u5024\u3092\u4e0e\u3048\u3066\u3044\u307e\u3059). \u6df1\u3044\u66f2\u304c\u3063\u305f\u8c37\u306e\u4e2d\u306b\u6700\u5c0f\u70b9\u304c\u3042\u308a, \u6700\u5c0f\u70b9\u306b\u5230\u9054\u3059\u308b\u306e\u304c\u96e3\u3057\u3044\u3068\u3055\u308c\u3066\u3044\u307e\u3059.<\/p>\n

10.3.1 VBA \u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f7f\u7528\u3057\u305f\u89e3\u304d\u65b9 (1)<\/h4>\n

Optif0<\/strong> \u3092\u4f7f\u3063\u305f\u30d7\u30ed\u30b0\u30e9\u30e0\u4f8b\u3092\u793a\u3057\u307e\u3059.<\/p>\n

\n
Sub F(N As Long, X() As Double, Fval As Double)\r\n    Fval = 100 * (X(1) - X(0) ^ 2) ^ 2 + (1 - X(0)) ^ 2\r\nEnd Sub\r\n\r\nSub Start()\r\n    Const NMax = 10, Ndata = 5\r\n    Dim N As Long, X(NMax) As Double, Xpls(NMax) As Double, Fpls As Double\r\n    Dim Info As Long, I As Long\r\n    N = 2\r\n    For I = 0 To Ndata - 1\r\n        '--- Input data\r\n        X(0) = Cells(6 + I, 1): X(1) = Cells(6 + I, 2)\r\n        '--- Find min point of equation\r\n        Call Optif0(N, X(), AddressOf F, Xpls(), Fpls, Info)\r\n        '--- Output result\r\n        Cells(6 + I, 3) = Xpls(0): Cells(6 + I, 4) = Xpls(1): Cells(6 + I, 5) = Info\r\n    Next\r\nEnd Sub<\/code><\/pre>\n<\/div>\n
\u76ee\u7684\u95a2\u6570\u3092\u5916\u90e8\u30b5\u30d6\u30eb\u30fc\u30c1\u30f3\u3068\u3057\u3066\u7528\u610f\u3057, \u521d\u671f\u5024\u3092\u6307\u5b9a\u3057\u3066 Optif0<\/strong> \u3092\u547c\u3073\u51fa\u3057\u307e\u3059. Optif0<\/strong> \u306f, \u521d\u671f\u5024\u3068\u3057\u3066\u4e0e\u3048\u3089\u308c\u305f\u8fd1\u4f3c\u89e3\u3092\u51fa\u767a\u70b9\u306b\u53cd\u5fa9\u8a08\u7b97\u3092\u884c\u3044, \u305d\u306e\u8fd1\u508d\u306e\u6700\u5c0f\u70b9\u3092\u6c42\u3081\u307e\u3059. \u3053\u3053\u3067\u306f, 5 \u3064\u306e\u7570\u306a\u308b\u521d\u671f\u5024\u3092\u4e0e\u3048\u305f\u3068\u304d\u306b\u3069\u306e\u3088\u3046\u306a\u89e3\u304c\u5f97\u3089\u308c\u308b\u304b\u3092\u898b\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u3068\u3057\u3066\u3044\u307e\u3059.<\/p>\n
\u521d\u671f\u5024\u3068\u3057\u3066\u306f, (-1.2, 1) \u306e\u4ed6\u306b (-1, 1),  (-1, -1), (0, 1), (0, 0) \u3092\u8a66\u3057\u3066\u307f\u307e\u3059.<\/p>\n
\u3053\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u5b9f\u884c\u3059\u308b\u3068, \u6b21\u306e\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3057\u305f.<\/p>\n
\"\"<\/p>\n
(-1, 1) \u306e\u3088\u3046\u306b\u521d\u671f\u5024\u306b\u3088\u3063\u3066\u306f\u53ce\u675f\u3057\u306a\u3044\u5834\u5408\u304c\u3042\u308a\u307e\u3057\u305f.<\/p>\n
10.3.2 VBA \u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f7f\u7528\u3057\u305f\u89e3\u304d\u65b9 (2)<\/h4>\n
\u30ea\u30d0\u30fc\u30b9\u30b3\u30df\u30e5\u30cb\u30b1\u30fc\u30b7\u30e7\u30f3\u7248 (RCI) \u306e Optif0_r<\/strong> \u3092\u4f7f\u3063\u305f\u30d7\u30ed\u30b0\u30e9\u30e0\u4f8b\u3092\u793a\u3057\u307e\u3059.<\/p>\n
\n
Sub Start()\r\n    Const NMax = 10, Ndata = 5\r\n    Dim N As Long, X(NMax) As Double, Xpls(NMax) As Double, Fpls As Double\r\n    Dim Info As Long, I As Long\r\n    Dim XX(NMax - 1) As Double, YY As Double, IRev As Long\r\n    N = 2\r\n    For I = 0 To Ndata - 1\r\n        '--- Input data\r\n        X(0) = Cells(6 + I, 1): X(1) = Cells(6 + I, 2)\r\n        '--- Find min point of equation\r\n        IRev = 0\r\n        Do\r\n            Call Optif0_r(N, X(), Xpls(), Fpls, Info, XX(), YY, IRev)\r\n            If IRev = 1 Then YY = 100 * (XX(1) - XX(0) ^ 2) ^ 2 + (1 - XX(0)) ^ 2\r\n        Loop While IRev <> 0\r\n        '--- Output result\r\n        Cells(6 + I, 3) = Xpls(0): Cells(6 + I, 4) = Xpls(1): Cells(6 + I, 5) = Info\r\n    Next\r\nEnd Sub<\/code><\/pre>\n<\/div>\n
\u76ee\u7684\u95a2\u6570\u3092\u5916\u90e8\u95a2\u6570\u3068\u3057\u3066\u4e0e\u3048\u308b\u306e\u3067\u306f\u306a\u304f, IRev = 1 \u306e\u3068\u304d\u306b XX() \u306e\u5024\u3092\u4f7f\u3063\u3066\u95a2\u6570\u5024\u3092\u8a08\u7b97\u3057 YY \u306b\u5165\u308c\u3066\u518d\u5ea6 Optif0_r<\/strong> \u3092\u547c\u3073\u51fa\u3057\u307e\u3059. RCI \u306e\u8a73\u7d30\u306b\u3064\u3044\u3066\u306f \u3053\u3061\u3089<\/a> \u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044.<\/p>\n
\u3053\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u5b9f\u884c\u3059\u308b\u3068\u4e0a\u3068\u540c\u3058\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059.<\/p>\n
10.3.3 \u30bd\u30eb\u30d0\u30fc\u3092\u4f7f\u7528\u3057\u305f\u89e3\u304d\u65b9<\/h4>\n
XLPack \u30bd\u30eb\u30d0\u30fc\u30a2\u30c9\u30a4\u30f3\u306e\u300c\u591a\u5909\u6570\u975e\u7dda\u5f62\u6700\u9069\u5316\u300d\u3092\u4f7f\u3063\u3066\u89e3\u304f\u3053\u3068\u3082\u3067\u304d\u307e\u3059. B9\u30bb\u30eb\u306b\u6570\u5f0f (=100*(C8-B8^2)^2+(1-B8)^2) \u304c\u5165\u529b\u3055\u308c\u3066\u3044\u307e\u3059.<\/p>\n
\"\"<\/p>\n
\u30bd\u30eb\u30d0\u30fc\u306b\u3064\u3044\u3066\u306f \u3053\u3061\u3089<\/a> \u3082\u53c2\u7167\u304f\u3060\u3055\u3044.<\/p>\n","protected":false},"excerpt":{"rendered":"
\u975e\u7dda\u5f62\u6700\u9069\u5316(\u591a\u5909\u6570)\u306e\u89e3\u6cd5\u3068XLPack\u3092\u4f7f\u3063\u305f\u89e3\u304d\u65b9<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[10],"tags":[],"class_list":["post-4778","post","type-post","status-publish","format-standard","hentry","category-tutorial"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/4778","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/comments?post=4778"}],"version-history":[{"count":5,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/4778\/revisions"}],"predecessor-version":[{"id":5164,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/4778\/revisions\/5164"}],"wp:attachment":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/media?parent=4778"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/categories?post=4778"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/tags?post=4778"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}