D.C.Approximation For Solving Second-order Cone Chanceconstrained Optimization Problems

Joint chance-constrained optimization problem is an important type of problem in the field of stochastic optimization.The methods of solving this kind of problem have attracted much attention.The representative methods are: convex approximation method,DC approximation method,smooth approximation method,etc.Many practical problems with important value,such as the stochastic European facility location problem,can be built as a stochastic second-order cone optimization problem.Due to the influence of uncertain factors,the constraint conditions are often required to be satisfied with a large probability in practical applications.So it can be modeled as a second-order cone chance-constrained optimization(SOCCCP)problem.This type of problem is usually non-convex and non-smooth,and the chance constraint usually does not have a closed expression.Based on the theory and algorithm of the joint chance-constraint optimization problem,the second-order cone chance-constrained optimization problem is transformed into a joint chance-constrained optimization problem by using eigenvalue function.D.C.approximation method for solving the second-order cone chance-constrained optimization problem is investigated in the thesis.The main research contents are as follows:The first chapter mainly introduces the research status of joint chance-constrained optimization problems and stochastic second-order cone optimization problems.Some preliminaries are presented.CVa R approximation problem and D.C.approximation problem of joint chance-constrained optimization problem are introduced in chapter 2.D.C.approximation of the second-order cone chance-constrained optimization(SOCCCP)problem is discussed in Chapter 3.Firstly,the properties and eigenvalue functions of the second-order cone are analyzed.Secondly,a second-order cone chance-constrained optimization(SOCCCP)model is constructed and transformed into a joint chance-constrained optimization(JCCP)model.Finally,equivalent D.C.approximation problem of(JCCP)is given.Chapter 4 studies the ?-approximation problem of the D.C.approximation problem.The algorithm framework of sequence convex approximation method for solving the ?-approximation problem and the convergence theorem of the algorithm are presented.