Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/6104
DC Field | Value | Language |
---|---|---|
dc.contributor | Department of Applied Mathematics | - |
dc.creator | Qi, HD | - |
dc.creator | Qi, L | - |
dc.creator | Sun, D | - |
dc.date.accessioned | 2014-12-11T08:28:20Z | - |
dc.date.available | 2014-12-11T08:28:20Z | - |
dc.identifier.issn | 1052-6234 | - |
dc.identifier.uri | http://hdl.handle.net/10397/6104 | - |
dc.language.iso | en | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.rights | © 2003 Society for Industrial and Applied Mathematics | en_US |
dc.subject | Variational inequality problem | en_US |
dc.subject | Constrained optimization | en_US |
dc.subject | Semismooth equation | en_US |
dc.subject | Trust region method | en_US |
dc.subject | Truncated conjugate gradient method | en_US |
dc.subject | Global and superlinear convergence | en_US |
dc.title | Solving Karush--Kuhn--Tucker Systems via the trust region and the conjugate gradient methods | en_US |
dc.type | Journal/Magazine Article | en_US |
dc.description.otherinformation | Author name used in this publication: Houduo Qi | en_US |
dc.identifier.spage | 439 | - |
dc.identifier.epage | 463 | - |
dc.identifier.volume | 14 | - |
dc.identifier.issue | 2 | - |
dc.identifier.doi | 10.1137/S105262340038256X | - |
dcterms.abstract | A popular approach to solving the Karush-Kuhn-Tucker (KKT) system, mainly arising from the variational inequality problem, is to reformulate it as a constrained minimization problem with simple bounds. In this paper, we propose a trust region method for solving the reformulation problem with the trust region subproblems being solved by the truncated conjugate gradient (CG) method, which is cost effective. Other advantages of the proposed method over existing ones include the fact that a good approximated solution to the trust region subproblem can be found by the truncated CG method and is judged in a simple way; also, the working matrix in each iteration is H, instead of the condensed H[sup T]H, where H is a matrix element of the generalized Jacobian of the function used in the reformulation. As a matter of fact, the matrix used is of reduced dimension. We pay extra attention to ensure the success of the truncated CG method as well as the feasibility of the iterates with respect to the simple constraints. Another feature of the proposed method is that we allow the merit function value to be increased at some iterations to speed up the convergence. Global and superlinear/quadratic convergence is shown under standard assumptions. Numerical results are reported on a subset of problems from the MCPLIB collection [S. P. Dirkse and M. C. Ferris, Optim. Methods Softw., 5 (1995), pp. 319-345]. | - |
dcterms.accessRights | open access | en_US |
dcterms.bibliographicCitation | SIAM journal on optimization, 2003, v. 14, no. 2, p. 439-463 | - |
dcterms.isPartOf | SIAM journal on optimization | - |
dcterms.issued | 2003 | - |
dc.identifier.isi | WOS:000187742000007 | - |
dc.identifier.scopus | 2-s2.0-2442467064 | - |
dc.identifier.eissn | 1095-7189 | - |
dc.identifier.rosgroupid | r19908 | - |
dc.description.ros | 2003-2004 > Academic research: refereed > Publication in refereed journal | - |
dc.description.oa | Version of Record | en_US |
dc.identifier.FolderNumber | OA_IR/PIRA | en_US |
dc.description.pubStatus | Published | en_US |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
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Qi_Solving_Karush_Kuhn.pdf | 269.46 kB | Adobe PDF | View/Open |
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