ERM Method For Stochastic Linear Complementarity Problem Of Second Order Cone

Stochastic optimization method, dated back to a century ago, is an effective modeling tool for optimization problems with random variables. The second order cone complementarity prob-lems (SOCCP) falls under the category of quilibrium optimization problems. In recent years, significant progress has been made on SOCCP research with the utilization of jordan algebra and spectral factorization. At this stage, both theory and practical application researches on SOCCP are on an upward trend, and the main research directions include:different smoothing methods to solve SOCCP problems, the existence of solution, the astringency of solution and their practical application directions. As the SOCCP problems are usually of various uncertain-ties, stochastic linear SOCCP problems are drawing more and more attention from researchers. The paper introduces expected residual minimization (ERM) method to solve linear SOCCP problems.The paper, consisting of 5 sections, mainly studies solution existence and astringency of stochastic linear SOCCP problem that have utilized ERM in the solving process.Section 1:A brief introduction to background information, including emergence and devel-opment of stochastic programming, models of stochastic complementarity problems, models of SOCCP problems, some research status and the practical application directions.Section2:A supply of some preliminary knowledge, including definition and main proper-ties of Euclidean jordan algebra, spectral decomposition theorems, lemmas required by conver-gence proof.Section3:An introduction to classical algorithms of four types of complementarity prob-lems, and three types of transformation models for stochastic linear complementarity problems transforming to problem solution of certainty in addition.Section4:An utilization of ERM method to solve stochastic linear SOCCP problems. The process is to transfer stochastic linear complementarity problems to minimization problems through second order cone complementarity FB function firstly, then prove solution existence and astringency of discrete objective function under the condition of reasonable assumption.In conclusion, by utilizing ERM method to solve stochastic linear SOCCP problems, the solution for discrete objective function is existent and convergent.