本文選題：隨機 + 二階錐互補問題　； 參考：《遼寧大學》2017年碩士論文

【摘要】：二階錐互補問題(SOCCP)是指在二階錐約束條件下兩組決策變量之間滿足一種“互補”關(guān)系,是一類均衡優(yōu)化問題.借助于歐幾里得若當代數(shù)技術(shù),近年來SOCCP得到了快速的發(fā)展.二階錐互補問題(SOCCP)在經(jīng)濟、工程等領(lǐng)域都有著廣泛的應(yīng)用.然而,現(xiàn)實生活中會存在一些不確定因素,忽視這些因素將會使決策失誤.為此,本文考慮隨機二階錐互補問題(SSOCCP).由于隨機變量的存在,隨機二階錐互補問題一般情況下無解.然而為了滿足含有隨機因素的實際問題對解的迫切要求,這需要我們構(gòu)造一個合理的確定性模型,再對該確定模型進行求解,并將該確定模型的解視為隨機二階錐互補問題的解.因此,為了得到隨機二階錐互補問題的合理的解,本文利用二階錐互補函數(shù)給出求解隨機二階錐互補問題的確定期望值(EV)模型.本文分別考慮應(yīng)用二階錐互補函數(shù)ΦT及ΦNR給出EV模型,并首先給出了該EV模型水平集有界的條件.當二階錐互補函數(shù)為ΦT時,本文首先討論了 EV模型目標函數(shù)的SC1性.由于該EV模型中含有數(shù)學期望,而期望不容易求得.為求解此模型,本文應(yīng)用樣本均值近似(SAA)方法給出此模型的近似問題.在理論上,本文進一步考慮了EV模型近似問題全局最優(yōu)解序列以及穩(wěn)定點序列的收斂性結(jié)果.當二階錐互補函數(shù)為ΦNR時,由于此時對應(yīng)的EV模型的目標函數(shù)是非光滑的,本文先利用光滑化方法給出相應(yīng)目標函數(shù)的光滑化函數(shù),并進一步應(yīng)用SAA方法給出近似問題.與ΦT對應(yīng)的EV模型類似,在理論上本文依然給出了當二階錐互補函數(shù)為ΦNR時,全局最優(yōu)解序列以及穩(wěn)定點序列的收斂性分析.最后,本文給出數(shù)值算例,并分別應(yīng)用所提方法求解.
[Abstract]:The second order cone complementarity problem (SOCCP) is a kind of "complementary" relation between two sets of decision variables under the condition of second-order conical constraint, and it is a kind of equilibrium optimization problem. With the aid of Euclidean modern numerical technology, SOCCP has been developed rapidly in recent years. Second order Cone complementarity problem (SOCCP) is widely used in economy, engineering and other fields. However, there are some uncertain factors in real life, and neglecting these factors will make decision-making mistakes. In this paper, we consider the stochastic second order cone complementarity problem. Because of the existence of random variables, there is no solution for the random second order cone complementarity problem. However, in order to meet the urgent need for the solution of practical problems with random factors, we need to construct a reasonable deterministic model and then solve the deterministic model. The solution of the model is regarded as the solution of the random second order cone complementarity problem. Therefore, in order to obtain a reasonable solution of the stochastic second-order cone complementarity problem, a definite expected value (EV) model for solving the stochastic second-order cone complementarity problem is given by using the second-order cone complementarity function. In this paper, the second order cone complementary function 桅 T and 桅 NR are used to give the EV model, and the bounded condition of the level set of the EV model is given. When the second order cone complementary function is 桅 T, we first discuss the SC1 property of the objective function of EV model. Because the EV model contains mathematical expectation, the expectation is not easy to get. In order to solve this model, the approximate problem of the model is given by using the sample mean approximation (SAA) method. In theory, the convergence results of the sequence of global optimal solutions and the sequence of stable points for the EV model approximation problem are further considered in this paper. When the second order cone complementary function is 桅 NR, the objective function of the corresponding EV model is non-smooth at this time. In this paper, the smoothing function of the corresponding objective function is given by using the smoothing method, and the approximate problem is given by using the SAA method. Similar to the EV model corresponding to 桅 T, the convergence analysis of the global optimal solution sequence and the stable point sequence is given when the second order cone complementary function is 桅 NR. Finally, numerical examples are given and solved by the proposed method.
【學位授予單位】：遼寧大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O221

【參考文獻】

相關(guān)碩士學位論文 前1條

1 申雪瑩;關(guān)于隨機互補問題的一類新模型[D];大連理工大學;2012年

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本文編號：1857753