In the particular case m = 0, i . e ., when there are no inequality constraints, the KKT conditions turn into the Lagrange conditions, and the KKT multipliers are called Lagrange multipliers.
22.
It was first discussed by Magnus Hestenes in 1969 and by entropic regularization, which gives rise to the " exponential method of multipliers, " a method that handles inequality constraints with a twice differentiable augmented Lagrangian function.
23.
With " v " the Lagrange multipliers on the non-negativity constraints, " ? " the multipliers on the inequality constraints, and " s " the slack variables for the inequality constraints.
24.
With " v " the Lagrange multipliers on the non-negativity constraints, " ? " the multipliers on the inequality constraints, and " s " the slack variables for the inequality constraints.
25.
The necessary conditions are sufficient for optimality if the objective function f of a maximization problem is a concave function, the inequality constraints g _ j are continuously differentiable convex functions and the equality constraints h _ i are affine functions.
26.
It is an interesting question, though, and I'm not sure of my last point; it may be just that problems arising in practice always have inequality constraints .-- talk ) 04 : 23, 1 July 2006 ( UTC)
27.
Where J is an objective, \ mathbf { x } is a vector of design variables, \ mathbf { g } is a vector of inequality constraints, \ mathbf { h } is a vector of equality constraints, and \ mathbf { x } _ { lb } and \ mathbf { x } _ { ub } are vectors of lower and upper bounds on the design variables.
28.
Then the fundamental theorem of linear inequalities implies ( for feasible problems ) that for every vertex "'x "'* of the LP feasible region, there exists a set of " d " ( or fewer ) inequality constraints from the LP such that, when we treat those " d " constraints as equalities, the unique solution is "'x "'*.
