Expected Value For Solving Stochastic Circular-Cone Complementarity Problems And Their Convergence Analysis

The circular-cone complementarity problem is a typical asymmetric cone comple-mentarity problem,which has many extensive applications in the fields of engineering,transportation,and economic equilibrium.However,in practical problems,it is often af-fected by uncertain factors such as weather,demand,and supply.If the influence of these uncertain factors is ignored,we will make wrong decisions.Therefore,it is important to study the stochastic circular-cone complementarity problem.The circular-cone complementary function is a powerful tool to solve the stochastic circular-cone complementary problem.The properties of the circular-cone complemen-tary function will directly affect a series of related properties such as the existence and convergence of the solution.Therefore,in Chapter 2,this paper introduces a circular-cone complementary function_N?_R,and constructs a circular-cone complementary function?_r.Since?_{N R}is non-smooth,and the smoothing function of?_{N R}needs to be used in the subsequent process of this article,so this paper constructs the smoothing function?^?_{N R}of?_{N R}.In general,due to the existence of random variables,the solution to the stochastic circular-cone complementarity problem usually does not exist.For this reason,scholars consider constructing a reasonable deterministic model,then solve it,and regard the obtained solution as the solution of the stochastic circular-cone complementarity problem.Based on this idea,this paper proposes the expected value(EV)model for solving the stochastic circular-cone complementarity problem.In Chapter 3,this paper proposes the EV model of the stochastic circular-cone complementarity problem when the circular-cone complementarity functions are?_rand?_{N R}respectively.When the circular-cone complementary function is?_r,since the EV model contains mathematical expectations,and mathematical expectations are not easy to calculate.In order to solve this problem,this paper presents the approximation problem of the EV model by using the sample average approximation method,and proves the convergence of the global optimal solution of the EV model and its approximate problem.When the circular-cone complementary function is?_{N R},since the objective function of the EV model is non-smooth,this paper uses the smoothing function to smooth the objective function.Furthermore,this paper also presents the approximation problem of the EV model by using the sample average approximation method,and proves the convergence of the global optimal solution of the EV model and its approximate problem.In addition,the EV model and its approximation problem are usually non-convex programming,it is difficult to find its global optimal solution,but its stable point can often be found,so it is very important to consider the convergence of the stable point.Therefore,this paper proves the convergence of the stable point of the smoothing sample average approximation problem of the EV model when?is fixed.