Solution of optimum gas allocation model for gas-lift block with sequential unconstrained minimization technique;

Based on the knowledge base of floating structure stability, the optimal design is performed by use of the mixing penalty function method, in which step optimization is combined with integral optimization, and the variable scale method is adopted for unconstrained minimization.

Method of mixed penalty function is used for the linear question, optimum prescription is obtained at the conditions in the paper.

This paper adopted the mixed penalty function method changing the restraint problem to the object function with penalty without restraint,when using the genetic algorithm to optimize the model and considering the characteristic of the model.

This paper adopt SUMT,set the mill′s relatively use of power as the optimization goal.

Half penalty method and optimism design of ten connecting bar mechanism of plunger slide in double action drawing press;

The essential boundary condition is imposed by employing a penalty method.

By using penalty method,Sobolev space,variational approach,partial differential equations,and function analysis theory,the optimal problem and the existence of the solution of the optimal regularized problem are obtained.