On the Analyticity of Underlying HKM Paths for Monotone Semidefinite Linear Complementarity Problems

C. K. Sim ()
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C. K. Sim: The Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2009, vol. 141, issue 1, No 11, 193-215

Abstract: 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 $\sqrt{\mu}$ , 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 $\sqrt{\mu}$ 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.

Keywords: Semidefinite linear complementarity problems; Ordinary differential equations; Off-central paths; HKM directions; Analyticity (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-008-9480-5

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