Переменная рассогласования

Переменная рассогласования — переменная, которая в задаче оптимизации добавляется к ограничению в виде неравенства[англ.] для преобразования его в равенство. Введение переменной рассогласования заменяет ограничение в виде неравенства ограничением в виде равенства в сочетании с ограничением неотрицательности переменной рассогласования[1].

Переменные рассогласования используются, в частности, в линейном программировании. Как и другие переменные в расширенных ограничениях, переменная рассогласования не может принимать отрицательные значения, поскольку алгоритм симплекс-метода требует, чтобы они были положительными или нулевыми[2].

Если переменная рассогласования, связанная с ограничением, равна нулю в конкретном решении-кандидате, то ограничение является обязательным для такого решения, поскольку ограничение распространяется на возможные изменения с этой точки. Если переменная рассогласования положительна в конкретном решении-кандидате, ограничение здесь необязательно, поскольку ограничение не ограничивает возможные изменения с этой точки. Если переменная рассогласования в какой-то момент отрицательна, точка области допустимых решений, поскольку она не удовлетворяет ограничению.

Переменные рассогласования также используются в методе Big M.

Например, за счёт введения переменной рассогласования неравенство может быть обращено в уравнение .

Примечания

  1. ↑ Boyd, Stephen P. Convex Optimization / Stephen P. Boyd, Lieven Vandenberghe. — Cambridge University Press, 2004. — ISBN 978-0-521-83378-3. Архивная копия от 9 мая 2021 на Wayback Machine
  2. ↑ Gärtner, Bernd; Matoušek, Jiří[англ.] (2006). Understanding and Using Linear Programming. Berlin: Springer. ISBN 3-540-30697-8.

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