Lagrange undetermined multiplier technique

The mathematical problem of locating a minimum on the seam between two energy surfaces is a constrained optimization, i.e., the energy should be minimized subject to the constraint that the reactant and product energies are equal. This may be handled, for example, by the technique of Lagrange undetermined multipliers, and optimization of the Lagrange function may be done by NR techniques ... 

The method of Lagrange s undetermined multipliers is a useful analytical technique for dealing with problems that have equality constraints (fixed design values). Examples of the use of this technique for simple design problems are given by Stoecker (1989), Peters and Timmerhaus (1991) and Boas (1963a). 

The numerical procedure used to solve the final equations The analytical method leads to a system of equations linear in the unknowns (i.e., the Lagrangian multipliers and their time derivatives up to order Therefore standard numerical techniques for solving such systems can be employed. The method of undetermined parameters leads to an additional system of equations generally nonlinear in the unknowns (i.e., the derivatives of the Lagrange multipliers of order s ,3x)- The order of nonlinearity depends on the particular... 

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