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https://doi.org/10.1007/s10107-006-0010-7
Title: | Underlying paths in interior point methods for the monotone semidefinite linear complementarity problem | Authors: | Sim, C.-K. Zhao, G. |
Issue Date: | Sep-2007 | Citation: | Sim, C.-K., Zhao, G. (2007-09). Underlying paths in interior point methods for the monotone semidefinite linear complementarity problem. Mathematical Programming 110 (3) : 475-499. ScholarBank@NUS Repository. https://doi.org/10.1007/s10107-006-0010-7 | Abstract: | An interior point method defines a search direction at each interior point of the feasible region. The search directions at all interior points together form a direction field, which gives rise to a system of ordinary differential equations (ODEs). Given an initial point in the interior of the feasible region, the unique solution of the ODE system is a curve passing through the point, with tangents parallel to the search directions along the curve. We call such curves off-central paths. We study off-central paths for the monotone semidefinite linear complementarity problem (SDLCP). We show that each off-central path is a well-defined analytic curve with parameter μ ranging over (0, ∞) and any accumulation point of the off-central path is a solution to SDLCP. Through a simple example we show that the off-central paths are not analytic as a function of √ μ and have first derivatives which are unbounded as a function of μ at μ = 0 in general. On the other hand, for the same example, we can find a subset of off-central paths which are analytic at μ = 0. These "nice" paths are characterized by some algebraic equations. © Springer-Verlag 2007. | Source Title: | Mathematical Programming | URI: | http://scholarbank.nus.edu.sg/handle/10635/104421 | ISSN: | 00255610 | DOI: | 10.1007/s10107-006-0010-7 |
Appears in Collections: | Staff Publications |
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