Given an

min f(x)

s.t. g_i(x) = 0, i=1..m

h_j(x) <= 0, j=1..p,

the Lagrangian function is

L = f(x) + \sum_i \alpha_i g_i(x) + \sum_j \beta_j h_j(x)

where \alpha_i is unconstrained, and \beta_j >= 0.

See more on Wikipedia.

__minimization__problemmin f(x)

s.t. g_i(x) = 0, i=1..m

h_j(x) <= 0, j=1..p,

the Lagrangian function is

L = f(x) + \sum_i \alpha_i g_i(x) + \sum_j \beta_j h_j(x)

where \alpha_i is unconstrained, and \beta_j >= 0.

See more on Wikipedia.

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