"Hamilton-Jacobi-Bellman equation" meaning in English

{
  "etymology_text": "Named after William Rowan Hamilton, Carl Gustav Jacob Jacobi, and Richard E. Bellman.",
  "forms": [
    {
      "form": "Hamilton-Jacobi-Bellman equations",
      "tags": [
        "plural"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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      "glosses": [
        "A nonlinear partial differential equation that provides necessary and sufficient conditions for optimality of a control with respect to a loss function."
      ],
      "id": "en-Hamilton-Jacobi-Bellman_equation-en-noun-xdS6gtX3",
      "links": [
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          "mathematics",
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          "nonlinear",
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        ],
        [
          "partial differential equation",
          "partial differential equation"
        ],
        [
          "optimality",
          "optimality"
        ],
        [
          "control",
          "control"
        ],
        [
          "loss function",
          "loss function"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A nonlinear partial differential equation that provides necessary and sufficient conditions for optimality of a control with respect to a loss function."
      ],
      "related": [
        {
          "word": "Bellman equation"
        },
        {
          "word": "Hamilton-Jacobi equation"
        }
      ],
      "synonyms": [
        {
          "tags": [
            "abbreviation"
          ],
          "word": "HJB equation"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Carl Gustav Jacob Jacobi",
        "Richard E. Bellman",
        "William Rowan Hamilton"
      ]
    }
  ],
  "word": "Hamilton-Jacobi-Bellman equation"
}

{
  "etymology_text": "Named after William Rowan Hamilton, Carl Gustav Jacob Jacobi, and Richard E. Bellman.",
  "forms": [
    {
      "form": "Hamilton-Jacobi-Bellman equations",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Bellman equation"
    },
    {
      "word": "Hamilton-Jacobi equation"
    }
  ],
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      "glosses": [
        "A nonlinear partial differential equation that provides necessary and sufficient conditions for optimality of a control with respect to a loss function."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
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          "nonlinear",
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        ],
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          "partial differential equation",
          "partial differential equation"
        ],
        [
          "optimality",
          "optimality"
        ],
        [
          "control",
          "control"
        ],
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          "loss function",
          "loss function"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A nonlinear partial differential equation that provides necessary and sufficient conditions for optimality of a control with respect to a loss function."
      ],
      "synonyms": [
        {
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            "abbreviation"
          ],
          "word": "HJB equation"
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      ],
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        "mathematics",
        "sciences"
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      "wikipedia": [
        "Carl Gustav Jacob Jacobi",
        "Richard E. Bellman",
        "William Rowan Hamilton"
      ]
    }
  ],
  "word": "Hamilton-Jacobi-Bellman equation"
}