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dc.contributor.authorQian, X.
dc.contributor.authorLiao, L.
dc.contributor.authorSun, Jie
dc.contributor.authorZhu, H.
dc.date.accessioned2018-08-08T04:42:18Z
dc.date.available2018-08-08T04:42:18Z
dc.date.created2018-08-08T03:50:45Z
dc.date.issued2018
dc.identifier.citationQian, X. and Liao, L. and Sun, J. and Zhu, H. 2018. The Convergent Generalized Central Paths for Linearly Constrained Convex Programming. SIAM Journal on Optimization. 28 (2): pp. 1183-1204.
dc.identifier.urihttp://hdl.handle.net/20.500.11937/69781
dc.identifier.doi10.1137/16M1104172
dc.description.abstract

The convergence of central paths has been a focal point of research on interior point methods. Quite detailed analyses have been made for the linear case. However, when it comes to the convex case, even if the constraints remain linear, the problem is unsettled. In [Math. Program., 103 (2005), pp. 63–94], Gilbert, Gonzaga, and Karas presented some examples in convex optimization, where the central path fails to converge. In this paper, we aim at finding some continuous trajectories which can converge for all linearly constrained convex optimization problems under some mild assumptions. We design and analyze a class of continuous trajectories, which are the solutions of certain ordinary differential equation (ODE) systems for solving linearly constrained smooth convex programming. The solutions of these ODE systems are named generalized central paths. By only assuming the existence of a finite optimal solution, we are able to show that, starting from any interior feasible point, (i) all of the generalized central paths are convergent, and (ii) the limit point(s) are indeed the optimal solution(s) of the original optimization problem. Furthermore, we illustrate that for the key example of Gilbert, Gonzaga, and Karas, our generalized central paths converge to the optimal solutions.

dc.publisherSociety for Industrial and Applied Mathematics
dc.relation.sponsoredbyhttp://purl.org/au-research/grants/arc/DP160102819
dc.titleThe Convergent Generalized Central Paths for Linearly Constrained Convex Programming
dc.typeJournal Article
dcterms.source.volume28
dcterms.source.number2
dcterms.source.startPage1183
dcterms.source.endPage1204
dcterms.source.issn1052-6234
dcterms.source.titleSIAM Journal on Optimization
curtin.departmentSchool of Electrical Engineering, Computing and Mathematical Science (EECMS)
curtin.accessStatusOpen access


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