Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/9511
Title: On the analyticity of underlying HKM paths for monotone semidefinite linear complementarity problems
Authors: Sim, CK
Keywords: Analyticity
HKM directions
Off-central paths
Ordinary differential equations
Semidefinite linear complementarity problems
Issue Date: 2009
Publisher: Springer
Source: Journal of optimization theory and applications, 2009, v. 141, no. 1, p. 193-215 How to cite?
Journal: Journal of optimization theory and applications 
Abstract: An interior point method (IPM) defines a search direction at an interior point of the feasible region. These search directions form a direction field, which in turn defines a system of ordinary differential equations (ODEs). The solutions of the system of ODEs are called off-central paths, underlying paths lying in the interior of the feasible region. It is known that not all off-central paths are analytic, whether w.r.t. μ or √μ, where μ represents the duality gap, at a solution of a given semidefinite linear complementarity problem, SDLCP (Sim and Zhao, Math. Program. 110:475-499, 2007). In Sim and Zhao (J. Optim. Theory Appl. 137:11-25, 2008), we give a necessary and sufficient condition for when an off-central path is analytic as a function of √μ at a solution of a general SDLCP. It is then natural to ask about the analyticity of a SDLCP off-central path at a solution, as a function of μ. We investigate this in the current paper. Again, we work under the assumption that the given SDLCP satisfies strict complementarity condition.
URI: http://hdl.handle.net/10397/9511
ISSN: 0022-3239
EISSN: 1573-2878
DOI: 10.1007/s10957-008-9480-5
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