【作者】 李亚杰；

【导师】 罗美菊；

【作者基本信息】 辽宁大学 ， 运筹学与控制论， 2017， 硕士

【摘要】 二阶锥互补问题(SOCCP)是指在二阶锥约束条件下两组决策变量之间满足一种“互补”关系,是一类均衡优化问题.借助于欧几里得若当代数技术,近年来SOCCP得到了快速的发展.二阶锥互补问题(SOCCP)在经济、工程等领域都有着广泛的应用.然而,现实生活中会存在一些不确定因素,忽视这些因素将会使决策失误.为此,本文考虑随机二阶锥互补问题(SSOCCP).由于随机变量的存在,随机二阶锥互补问题一般情况下无解.然而为了满足含有随机因素的实际问题对解的迫切要求,这需要我们构造一个合理的确定性模型,再对该确定模型进行求解,并将该确定模型的解视为随机二阶锥互补问题的解.因此,为了得到随机二阶锥互补问题的合理的解,本文利用二阶锥互补函数给出求解随机二阶锥互补问题的确定期望值(EV)模型.本文分别考虑应用二阶锥互补函数ΦT及ΦNR给出EV模型,并首先给出了该EV模型水平集有界的条件.当二阶锥互补函数为ΦT时,本文首先讨论了 EV模型目标函数的SC1性.由于该EV模型中含有数学期望,而期望不容易求得.为求解此模型,本文应用样本均值近似(SAA)方法给出此模型的近似问题.在理论上,本文进一步考虑了EV模型近似问题全局最优解序列以及稳定点序列的收敛性结果.当二阶锥互补函数为ΦNR时,由于此时对应的EV模型的目标函数是非光滑的,本文先利用光滑化方法给出相应目标函数的光滑化函数,并进一步应用SAA方法给出近似问题.与ΦT对应的EV模型类似,在理论上本文依然给出了当二阶锥互补函数为ΦNR时,全局最优解序列以及稳定点序列的收敛性分析.最后,本文给出数值算例,并分别应用所提方法求解.更多还原

【Abstract】 The second-order-cone complementarity problems (SOCCP) are a kind of equilibri-um optimization problems. The two sets of decision variables satisfy a “complementary relationship" under the conditions of second-order-cone constraints. With the help of Eu-clidean Jordan algebra technique, in recent years, the second-order-cone complementarity problems have rapid development. The second-order-cone complementarity problems have widely applications in economic, engineering and other fields. However, there are some uncertain factors in real life. Ignoring these factors will lead to decision-making errors.Hence, in this paper, we consider stochastic second-order-cone complementarity problems(SSOCCP).Because of the existence of random variables, the stochastic second-order-cone com-plementarity problems may have no solution in general. However, in order to satisfy the urgent need of solving the practice problems with random factors, it is necessary to con-struct a reasonable deterministic model, then to solve the deterministic model and the solution of the deterministic model is regarded as the solution of the stochastic second-order-cone complementarity problems. Hence, in order to obtain the reasonable solution of the stochastic second-order-cone complementarity problems, we use the second-order-cone complementary functions to give a deterministic expected value (EV) model of stochastic second-order-cone complementarity problems.In this paper, we consider to use the second-order-cone complement functions φT, andφNR to give the EV model, and first give the boundedness of the level set of the EV model. When the second-order-cone complementarity function is φT, we first discuss the SC1 property of the objective function of the EV model. Since the EV model contains an expectation function, and the expectation is not easy to get. For solving this model, we employ sample average approximation (SAA) method to give approximation problems of the EV model. In theory, the convergence results of global solutions sequence and station?ary points sequence for the corresponding approximation problems are considered. When the second-order-cone complementarity function is φNR, because the objective function of EV model is non-smooth, we first use the smoothing method to give the smoothing func-tion of the corresponding objective function. We then employ SAA method to give the approximation problems. Similar to EV model of the case that complementarity problem is φT, in theory, the convergence results of global solutions sequence and stationary points sequence for the approximation problems while the complementarity problem is φNR are also considered. Finally, in this paper the numerical experiments are given and solved by the proposed method.更多还原