Algorithm Research On A Class Of Unconstrained Stochastic Optimization Problems

Stochastic optimization is an important branch of mathematical optimization,which is widely used in management science,information engineering,economics,optimal control agriculture and industrial engineering.This paper mainly studies a kind of stochastic unconstrained optimization problem and its algorithm.Its problem model is often used in the fields of engineering,economics and operational research.The structure and main research contents of this paper are summarized as follows:The first chapter introduces the basic situation of a kind of unconstrained stochastic optimization problems,including the concept,research status and significance of this kind of stochastic optimization problems,as well as several classical stochastic optimization algorithms and their development,and introduces a special form of this kind of problems-non derivative optimization problems,and gives the relevant algorithm analysis.Finally,the main research work of this paper is introduced.In the second chapter,we give an efficient stochastic trust region algorithm for large-scale nonconvex problems,and prove its convergence.Related numerical experiments show that the stochastic trust region algorithm can not only solve largescale ill posed problems and nonconvex problems,but also has fast convergence speed and excellent numerical performance.In the third chapter,we study the problem that derivative information is not available and function value calculation is noisy.We propose a random non derivative algorithm based on trust region framework.The algorithm uses sparse recovery theory to construct a complete quadratic model,and combines trust region algorithm to solve the random problem.Finally,the second-order convergence results of the algorithm are given,and it is proved that the algorithm converges to a second-order stable point with a probability close to 1 under certain assumptions.Finally,the conclusion and prospect of this paper are given.