Asymptotic Behavior of Underlying NT Paths in Interior Point Methods for Monotone Semidefinite Linear Complementarity Problems
Copyright policy )Asymptotic Behavior of Underlying NT Paths in Interior Point Methods for Monotone Semidefinite Linear Complementarity Problems
This article studies off-central paths, corresponding to the Nesterov-Todd (NT) direction for the solution of the semidefinite linear complementarity problem. The article begins with a literature overview covering prior work on interior methods, central paths, convergence and the properties of semidefinite programs and monotone semidefinite linear complementarity problems. The second section contains the main definitions and the background assumptions required for this problem. This is followed by the main section of the paper, where the asymptotic behavior of NT paths are studied. Several important theorems are presented in this section with proof, including the necessary and sufficient conditions for when such a path is analytic with respect to \(\mu\) and \(\sqrt\mu\). The paper concludes with a list of relevant articles.
- Hong Kong Polytechnic University China (People's Republic of)
- University of Portsmouth United Kingdom
- Hong Kong Polytechnic University (香港理工大學) Hong Kong
- Hong Kong Polytechnic University (香港理工大學) China (People's Republic of)
330, 000, interior point methods, NT direction, Semidefinite linear complementarity problem, Interior-point methods, 510, ordinary differential equations, local convergence, Semidefinite programming, Interior point methods, Local convergence, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming), Ordinary differential equations, semidefinite linear complementarity problem
330, 000, interior point methods, NT direction, Semidefinite linear complementarity problem, Interior-point methods, 510, ordinary differential equations, local convergence, Semidefinite programming, Interior point methods, Local convergence, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming), Ordinary differential equations, semidefinite linear complementarity problem
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