Initializing help system before first use

Minimum values

y = min{x1, x2} for two continuous variables x1, x2

  • Must know lower and upper bounds

    L1 ≤ x1 ≤ U1 [1.1]
    L2 ≤ x2 ≤ U2 [1.2]

  • Introduce binary variables d1, d2 to mean

    di 1 if xi is the minimum value;
    0 otherwise

  • MIP formulation:

    y ≤ x1 [2.1]
    y ≤ x2 [2.2]
    y ≥ x1 - (U1 - Lmin)(1 - d1) [3.1]
    y ≥ x2 - (U2 - Lmin)(1 - d2) [3.2]
    d1 + d2 = 1 [4]

  • Generalization to y = min{x1, x2, ..., xn}

    Li ≤ xi ≤ Ui [1.i]
    y ≤ xi [2.i]
    y ≥ xi - (Ui - Lmin)(1 - di) [3.i]
    ∑i di = 1 [4]

Parent Topic Binary variables

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