【摘要】：二階錐互補問題(SOCCP)作為一類具有普遍意義的均衡優(yōu)化問題,近年來備受關(guān)注.學(xué)者們將歐幾里得若當代數(shù)與譜分解作為工具,使得二階錐互補問題的研究取得重大進展.目前,有關(guān)確定性二階錐互補問題的研究在理論和實際應(yīng)用方面都有良好的發(fā)展趨勢,理論方面的主要研究方向有:SOCCP的各類光滑化問題的求解、有關(guān)解的存在性與收斂性分析以及一些有效算法的開發(fā)研究等.實際應(yīng)用方面,許多問題均可轉(zhuǎn)化為二階錐互補問題,例如三維摩擦接觸問題、魯棒納什均衡問題等.然而,實際問題往往包含諸如價格、供應(yīng)、需求等不確定因素,忽略這些隨機因素將導(dǎo)致嚴重的后果.由于隨即變量的引入,使得隨機二階錐互補問題比二階錐互補問題更復(fù)雜,進而在實際方面也有更加廣泛的應(yīng)用.因此,隨機二階錐互補問題的相關(guān)研究是十分必要且意義重大.基于上述原因,本文提出了求解隨機二階錐互補問題的條件風險價值(CVaR)模型.本文將二階錐互補函數(shù)作為損失函數(shù),結(jié)合光滑化方法和蒙特卡羅樣本均值近似方法給出隨機二階錐互補問題(SSOCCP)的CVaR光滑化模型以及CVaR光滑化樣本均值近似模型,進一步對對應(yīng)光滑化問題及光滑近似問題進行收斂性分析,并且給出相關(guān)的數(shù)值算例并應(yīng)用所提出的方法進行求解.最后,對本文所研究的主要內(nèi)容進行詳細的總結(jié),并對SSOCCP的條件風險價值模型提出進一步的假設(shè)和展望.
[Abstract]:The second order cone complementarity problem (SOCCP), as a universal equilibrium optimization problem, has attracted much attention in recent years. By using Euclidean number and spectral decomposition as tools, great progress has been made in the study of second-order cone complementarity problem. At present, the research on deterministic second-order cone complementarity problem has a good development trend in theory and practical application. The main research directions of theory are: solving various smoothing problems of SOCCP. The existence and convergence of solutions and the development of some effective algorithms are discussed. In practical applications, many problems can be transformed into second-order cone complementarity problems, such as three-dimensional frictional contact problems, robust Nash equilibrium problems and so on. However, practical problems often include uncertain factors such as price, supply, demand and so on. Ignoring these random factors will lead to serious consequences. Because of the introduction of random variables, the random second-order cone complementarity problem is more complex than the second-order cone complementarity problem, and it is also widely used in practice. Therefore, it is necessary and significant to study the random second order cone complementarity problem. Based on the above reasons, this paper presents a conditional risk value (CVaR) model for solving stochastic second-order cone complementarity problems. In this paper, the second order cone complementary function is taken as the loss function, and the CVaR smoothing model and the CVaR smoothing sample mean approximation model for the stochastic second order cone complementarity problem (SSOCCP) are given by combining the smoothing method and the Monte Carlo sample mean approximation method. Furthermore, the convergence of the corresponding smoothing problem and the smooth approximation problem is analyzed, and the numerical examples are given and solved by the proposed method. Finally, the main contents of this paper are summarized in detail, and further hypotheses and prospects for the conditional risk value model of SSOCCP are put forward.
【學(xué)位授予單位】：遼寧大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O221

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本文編號：2401578