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

dc.contributor 陳界山 zh_TW
dc.contributor Chen, Jein-Shan en_US
dc.contributor.author 阮成昭 zh_TW
dc.contributor.author Nguyen Thanh Chieu en_US
dc.date.accessioned 2019-09-05T01:07:07Z
dc.date.available 不公開
dc.date.available 2019-09-05T01:07:07Z
dc.date.issued 2019
dc.description.abstract 無中文摘要 zh_TW
dc.description.abstract In 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.identifier G080540005S
dc.identifier.uri http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22G080540005S%22.&%22.id.&
dc.identifier.uri http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/101599
dc.language 英文
dc.subject Second-order cone zh_TW
dc.subject Absolute value equations zh_TW
dc.subject Smoothing Newton algorithm zh_TW
dc.subject Penalty and barrier method zh_TW
dc.subject Asymptotic function zh_TW
dc.subject Convex analysis zh_TW
dc.subject Smoothing function zh_TW
dc.subject Second-order cone en_US
dc.subject Absolute value equations en_US
dc.subject Smoothing Newton algorithm en_US
dc.subject Penalty and barrier method en_US
dc.subject Asymptotic function en_US
dc.subject Convex analysis en_US
dc.subject Smoothing function en_US
dc.title Applications of Smoothing Functions for Solving Optimization Problems Involving Second-Order Cone zh_TW
dc.title Applications of Smoothing Functions for Solving Optimization Problems Involving Second-Order Cone en_US
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