Some Research Work About Stochastic Optimization Problems

This report is concerned with the stochastic optimization problems. Firstly, we propose a kind of stochastic knapsack feasibility problem, which is defined in a probability space. When the probability space only contains a single realization, the stochastic knapsack feasibility problem reduces to the well-known NP-hard knapsack feasibility problem. Two equivalent formulations of the proposed stochastic knapsack feasibility problem are also given. Secondly, we consider the definitions and properties of some kinds of stochastic structured tensors. The stochastic structured tensor complementarity problems are given. Finally, based on the expected residual minimization formulation (ERM) of the stochastic structured tensor complementarity problems, two kinds of optimization methods are proposed for solving the stochastic structured tensor complementarity problems.