The Research Of Fast-lipschitz Optimization

This thesis focuses on Fast-Lipschitz optimization.This is a special case of distributed optimization proposed by C.Fischion in 2011.Fast-Lipschitz optimization is a framework for solving optimization problems.This framework mainly considers some specific problem structures.The optimal solution of the problem is obtained by a system of equations,and it is easy to obtain the optimal solution by the fixed point iterative method.Typical application areas such as wireless sensor networks.The specific content of this article is as follows:First,based on the researches of Martin Jakobsson and Carlo Fischione,this thesis presents the generalized Fast-Lipschitz optimization problem and gives the qualification conditions for the generalized Fast-Lipschitz optimization problem.Based on the K-K-T condition,the existence and uniqueness of the optimal solution of the generalized Fast-Lipschitz optimization problem under the qualification condition are proved.An example is given to illustrate that the generalized Fast-Lipschitz optimization framework indeed promotes C.Fischion's Fast-Lipschitz optimization framework.Secondly,for the two cases with fewer constraints than the decision variables and the absence of variables in the objective function,the generalized Fast-Lipschitz framework was introduced into the relaxation condition.Finally,in order to compare the convergence speed between the generalized Fast-Lipschitz optimization algorithm and the traditional Lagrangian algorithm,Defines the spectral radius as the variable of the convergence rate,and gives the general condition that the generalized Fast-Lipschitz optimization algorithm is faster than the Lagrangian method.