Lagrangian multipliers

Lagrangian multipliers

[lə′grän·jē·ən ′məl·tə‚plī·ərz]
(mathematics)
A technique whereby potential extrema of functions of several variables are obtained. Also known as undetermined multipliers.
References in periodicals archive ?
Each iteration includes four steps: first, convert the optimal problem into a dual problem and find the dual solution of the dual problem; secondly, update the Lagrangian multipliers by the subgradient algorithm; thirdly, based on the updated Lagrangian multipliers , find the feasible solution for the primal optimal problem to obtain the upper bound; fourthly, check whether the duality gap between the feasible solution and the dual solutions achieve some value or the maximum iteration time arrives.
The unconstrained Lagrangian multipliers [[lambda].
t](i)} as the Lagrangian multipliers of constraints (A.
2), (3) and (4) are the three possible constraints, which can be relaxed using the respective Lagrangian multipliers.
The Lagrangian multipliers are given in brackets to the fight of the constraints, where the Lagrangian function can be written as:
Vlase, "Elimination of lagrangian multipliers," Mechanics Research Communications, vol.
The linear system (13) can be solved within the inner product (15) expressed by the Gaussian kernel (16), and then the parameter [beta] and the Lagrangian multipliers [[lambda].
The primal subproblem generates the Lagrangian multipliers ([[bar.
A LaGrangian Multiplier Approach to the Solution of a Special Constrained Matrix Problem," Journal of Regional Science, 20, 1980, pp.
2] is a Lagrangian multiplier, and the resulting first-order conditions are