Applications of Smoothing Functions for Solving Optimization Problems Involving Second-Order Cone

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dc.contributor陳界山zh_TW
dc.contributorChen, Jein-Shanen_US
dc.contributor.author阮成昭zh_TW
dc.contributor.authorNguyen Thanh Chieuen_US
dc.date.accessioned2019-09-05T01:07:07Z
dc.date.available不公開
dc.date.available2019-09-05T01:07:07Z
dc.date.issued2019
dc.description.abstract無中文摘要zh_TW
dc.description.abstractIn this thesis, we apply smoothing methods for solving two optimization problems over a second-order cone, namely the absolute value equation associated with second-order cone (abbreviated as SOCAVE) and convex second-order cone programming (abbreviated as CSOCP). For SOCAVE, numerical comparisons are presented to illustrate the kind of smoothing functions which work well along with the smoothing Newton algorithm. In particular, the numerical experiments show that the well-known loss function widely used in engineering community is the worst one among the constructed smoothing functions. It indicates that other proposed smoothing functions can be considered for solving engineering problems. For CSOCP, we use the penalty and barrier functions as smoothing functions. These methods are motivated by the work presented in [2]. Under the usual hypothesis that the CSOCP has a nonempty and compact optimal set, we show that the penalty and barrier problems also have a nonempty and compact optimal set. Moreover, any sequence of approximate solutions of these penalty and barrier problems is shown to be bounded whose accumulation points are solutions of the CSOCP. Finally, we provide numerical simulations to illustrate the theoretical results. More specifically, we use various penalty and barrier functions in solving the CSOCP and compare their efficiency by means of performance profiles.en_US
dc.description.sponsorship數學系zh_TW
dc.identifierG080540005S
dc.identifier.urihttp://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22G080540005S%22.&%22.id.&
dc.identifier.urihttp://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/101599
dc.language英文
dc.subjectSecond-order conezh_TW
dc.subjectAbsolute value equationszh_TW
dc.subjectSmoothing Newton algorithmzh_TW
dc.subjectPenalty and barrier methodzh_TW
dc.subjectAsymptotic functionzh_TW
dc.subjectConvex analysiszh_TW
dc.subjectSmoothing functionzh_TW
dc.subjectSecond-order coneen_US
dc.subjectAbsolute value equationsen_US
dc.subjectSmoothing Newton algorithmen_US
dc.subjectPenalty and barrier methoden_US
dc.subjectAsymptotic functionen_US
dc.subjectConvex analysisen_US
dc.subjectSmoothing functionen_US
dc.titleApplications of Smoothing Functions for Solving Optimization Problems Involving Second-Order Conezh_TW
dc.titleApplications of Smoothing Functions for Solving Optimization Problems Involving Second-Order Coneen_US

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