Smoothing Method For Solving Second-order Cone Chance Constrained Optimization Problems

Many practical problems with important value can be modeled as stochastic second-order cone programming problems due to the existence of uncertain factors.In practical applications,constraints often need to be satisfied with a large probability.For example,the power system must be operated safely under a certain degree of credibility in new energy power systems.So it can be modeled as a second-order cone chance constrained optimization problem,which is usually non-convex and non-smooth.This paper mainly discusses the smoothing method for solving the second-order cone chance constrained optimization problem.Using the eigenvalue function,the second-order cone chance constrained optimization problem is transformed into a joint chance constrained optimization problem.Based on a class of smooth functions,a smooth conservative approximation problem is constructed,and an algorithm framework for solving the smooth approximation problem is given.The main research results are as follows:The first chapter aims at summarizing the research status of chance constrained optimization problem and the second-order cone optimization problem.Some preliminaries used later are introduced.Basic algebraic properties of the second-order cone are discussed in chapter 2.Through the Euclidean Jordan algebra and spectral decomposition,the relationship between the vectors in the second-order cone and its eigenvalues is established.Consequently,the second-order cone chance constrained optimization model is transformed into a joint Chance constrained optimization model.A class of smooth approximation function φ(λ(x,ξ),t)of the characteristic function 1(0,+∞)(λ(x,ξ))are constructed in chapter 3.And the smooth approximation problem of the chance constrained optimization problem is built based on function φ(λ(x,ξ),t).Theε-approximation problem of the smooth approximation problem is discussed,and the convergence is analyzed when parameter ε tends to 0.Sequential convex approximation(SCA)method for solving ε-approximation problems and inexact sequential convex approximation(ISCA)algorithm are described in chapter 4.The convergence of the algorithm is proved.