Research On Smooth Algorithms For Constrained Optimization Problem

Constrained optimization problem is a kind of optimization problems to find the optimal solution under constraints.It has been widely used in the fields of natural science,economy,engineering and related fields.With the deepening of researchers’research on unknown fields,the application scope of constrained optimization problem is expanding and integrated into more and more research fields,such as signal recovery in compressed sensing,real-time pricing of smart grid,etc.In this thesis,the smoothing methods of constrained optimization are studied.The main research contents are as follows:（1）The constrained optimization problem and the solution methods of constrained optimization problem are summarized in this thesis.And the solution method of the general structural constrained optimization problem is studied.The penalty function construction process and smoothing process of the general structural constrained optimization problem are studied,a new smoothing Broyden-Fletcher-Goldfarb-Shanno（BFGS）method is given,and the global convergence analysis of the method is also given.The numerical experimental results show the effectiveness of the method.（2）The method of constrained optimization problem with l₁-norm is studied.This thesis introduces the constrained optimization problem with l₁-norm,gives the smoothing process of the constrained optimization problem with l₁-norm and a new smoothing conjugate gradient method.The global convergence of the method is also given.The relevant numerical experimental results show the effectiveness of the method.（3）The real-time pricing constraint optimization problem of smart grid based on social benefit maximization is studied.Aiming at the practical application of convex constrained optimization problem in smart grid,the constrained optimization problem is smoothed based on Fischer-Burmeister（FB）function,and a new smoothing conjugate gradient method is proposed.The global convergence of the method is proved under general assumptions,and the relevant numerical simulation experiments also show the effectiveness of the method.