Based on the essence of generalized Lagrange multiplier,a fictitious domain method,especially for Poisson problems,is proposed,where all computational tasks are carried out in an auxiliary simply shaped domain,and the original domain is embedded into.

The results show that the algorithmic programme is of a faster convergent speed and a higher solving precision with an augmented lagrangian method which is more suitable for the optimization than penalty function method.

Optimization of integral flange by Lagrangian method.;

In the new method,the Lagrangian method with inequality restriction is used to assign the load between the monoblock so as to increase the feasibility a.

The dynamic equations were derived applying the Lagrangian multiplier method.

Discussion of solving the problem of motionless michanics by Lagrangian multiplier;

Hybrid finite element method constrained by Lagrange multiplier in couple-stress theory;

The constrained problem can be changed to a non-constrained problem by introducing Lagrange multipliers.

In order to decrease the picture quality fluctuation due to Q2 rate-control scheme in low rate and low delay video communication,firstly,a target bit-allocation algorithm was proposed with Lagrange multiplier method,where the coding information of previous one frame and the buffer status were taken into account.