ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 30 Nov 2021 13:27:09 GMT2021-11-30T13:27:09Z5051- Underlying paths and local convergence behaviour of path-following interior point algorithm for SDLCP and SOCPhttps://scholarbank.nus.edu.sg/handle/10635/14433Title: Underlying paths and local convergence behaviour of path-following interior point algorithm for SDLCP and SOCP
Authors: SIM CHEE KHIAN
Abstract: We present a new way to view the off-central path in path-following interior point method for monotone semidefinite linear complementarity problem (SDLCP) and second order cone programming (SOCP). Using this definition, we show the existence of off-central path for SDLCP for general direction. Restricting to a particular direction, we analyse a simple SDP example to show that not all off-central paths are analytic at the optimal solution. We then investigate its implication on the local convergence behaviour of first-order predictor-corrector algorithm. We also give a necessary and sufficient condition for off-central path for general SDLCP to be analytic at the limit point when \mu = 0. Next, we show the existence of off-central path for SOCP for a particular direction. We then investigate asymptotic properties, for example, strict complementarity convergence, asymptotic analyticity, of these off-central paths.
Fri, 21 Jan 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/144332005-01-21T00:00:00Z
- A note on the Lipschitz continuity of the gradient of the squared norm of the matrix-valued Fischer-Burmeister functionhttps://scholarbank.nus.edu.sg/handle/10635/44039Title: A note on the Lipschitz continuity of the gradient of the squared norm of the matrix-valued Fischer-Burmeister function
Authors: SIM CHEE KHIAN; Sun, J.; Ralph, D.
Abstract: Based on a formula of Tseng, we show that the squared norm of the matrix-valued Fischer-Burmeister function has a Lipschitz continuous gradient.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/440392006-01-01T00:00:00Z
- Asymptotic behavior of Helmberg-Kojima-Monteiro (HKM) paths in interior-point methods for monotone semidefinite linear complementarity problems: General theoryhttps://scholarbank.nus.edu.sg/handle/10635/102888Title: Asymptotic behavior of Helmberg-Kojima-Monteiro (HKM) paths in interior-point methods for monotone semidefinite linear complementarity problems: General theory
Authors: SIM CHEE KHIAN; Zhao, G.
Abstract: An interior-point method (IPM) defines a search direction at each interior point of the feasible region. These search directions form a direction field, which in turn gives rise to a system of ordinary differential equations (ODEs). Thus, it is natural to define the underlying paths of the IPM as the solutions of the system of ODEs. In Sim and Zhao (Math. Program. Ser. A, [2007], to appear), these off-central paths are shown to be well-defined analytic curves and any of their accumulation points is a solution to the given monotone semidefinite linear complementarity problem (SDLCP). Off-central paths for a simple example are also studied in Sim and Zhao (Math. Program. Ser. A, [2007], to appear) and their asymptotic behavior near the solution of the example is analyzed. In this paper, which is an extension of Sim and Zhao (Math. Program. Ser. A, [2007], to appear), we study the asymptotic behavior of the off-central paths for general SDLCPs using the dual HKM direction. We give a necessary and sufficient condition for when an off-central path is analytic as a function of √μ at a solution of the SDLCP. Then, we show that, if the given SDLCP has a unique solution, the first derivative of its off-central path, as a function of √μ, is bounded. We work under the assumption that the given SDLCP satisfies the strict complementarity condition. © 2007 Springer Science+Business Media, LLC.
Tue, 01 Apr 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1028882008-04-01T00:00:00Z
- Inexact subgradient methods for quasi-convex optimization problemshttps://scholarbank.nus.edu.sg/handle/10635/128073Title: Inexact subgradient methods for quasi-convex optimization problems
Authors: Hu Y.; Yang X.; Sim C.-K.
Thu, 01 Jan 2015 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1280732015-01-01T00:00:00Z
- A note on treating a second order cone program as a special case of a semidefinite programhttps://scholarbank.nus.edu.sg/handle/10635/102717Title: A note on treating a second order cone program as a special case of a semidefinite program
Authors: SIM CHEE KHIAN; Zhao, G.
Abstract: It is well known that a vector is in a second order cone if and only if its "arrow" matrix is positive semidefinite. But much less well-known is about the relation between a second order cone program (SOCP) and its corresponding semidefinite program (SDP). The correspondence between the dual problem of SOCP and SDP is quite direct and the correspondence between the primal problems is much more complicated. Given a SDP primal optimal solution which is not necessarily "arrow-shaped", we can construct a SOCP primal optimal solution. The mapping from the primal optimal solution of SDP to the primal optimal solution of SOCP can be shown to be unique. Conversely, given a SOCP primal optimal solution, we can construct a SDP primal optimal solution which is not an "arrow" matrix. Indeed, in general no primal optimal solutions of the SOCP-related SDP can be an "arrow" matrix. © Springer-Verlag 2004.
Fri, 01 Apr 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1027172005-04-01T00:00:00Z