【摘要】：摘要:本論文主要研究了集值擬變分不等式問(wèn)題的間隙函數(shù)和誤差界,集值混合變分不等式問(wèn)題的投影算法.全文共分三個(gè)章節(jié),具體內(nèi)容如下:第一章,分別介紹了本文的研究背景、現(xiàn)狀及主要內(nèi)容.第二章,首先研究了集值擬變分不等式的間隙函數(shù),然后利用該間隙函數(shù)建立了集值擬變分不等式與優(yōu)化問(wèn)題間的等價(jià)關(guān)系.最后,通過(guò)這一等價(jià)關(guān)系討論了集值擬變分不等式的誤差界問(wèn)題.第三章,提出了一種集值混合變分不等式新的投影算法.在迭代的每一步,首先利用當(dāng)前點(diǎn)xi,通過(guò)計(jì)算預(yù)解算子得到點(diǎn)zi,其中的迭代步長(zhǎng)滿(mǎn)足某種Armjo線(xiàn)搜索.然后,利用zi構(gòu)造出分離當(dāng)前點(diǎn)xi及集值混合變分不等式解集的超平面,再將當(dāng)前點(diǎn)向該超平面做投影得到下一步迭代點(diǎn).在一定的條件下,給出了該算法產(chǎn)生的無(wú)窮序列具有全局收斂性.最后,給出了算法的數(shù)值計(jì)算結(jié)果.
[Abstract]:Absrtact: in this paper, the gap function and error bound for set-valued quasi-variational inequality problems and the projection algorithm for set-valued mixed variational inequality problems are studied. This paper is divided into three chapters. The main contents are as follows: the first chapter introduces the research background, current situation and main contents of this paper. In the second chapter, the gap function of set-valued quasi variational inequality is studied, and then the equivalent relation between the set valued quasi variational inequality and the optimization problem is established by using the gap function. Finally, the error bound problem of set-valued quasi variational inequalities is discussed by using this equivalence relation. In chapter 3, a new projection algorithm for set-valued mixed variational inequalities is proposed. In each step of the iteration, the point zi, is obtained by calculating the resolvent operator using the current point xi,. The iteration step size satisfies some Armjo line search. Then, using zi to construct the hyperplane that separates the current point xi and the solution set of the set-valued mixed variational inequality, and then projecting the current point to the hyperplane to get the next iteration point. Under certain conditions, the global convergence of the infinite sequence generated by the algorithm is given. Finally, the numerical results of the algorithm are given.
【學(xué)位授予單位】：四川師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O178

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相關(guān)期刊論文 前3條

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本文編號(hào)：2219138