Quadratic convergence in a primal-dual method
Mathematics of Operations Research
A quadratically convergent OnL -iteration algorithm for linear programming
Mathematical Programming: Series A and B
On quadratic and OnL convergence of a predictor-corrector algorithm for LCP
Mathematical Programming: Series A and B
The projective method for solving linear matrix inequalities
Mathematical Programming: Series A and B
Self-scaled barriers and interior-point methods for convex programming
Mathematics of Operations Research
Local convergence of predictor-corrector infeasible-interior-point algorithms for SDPs and SDLCPs
Mathematical Programming: Series A and B
On Two Interior-Point Mappings for Nonlinear Semidefinite Complementarity Problems
Mathematics of Operations Research
Superlinear convergence of interior-point algorithms for semidefinite programming
Journal of Optimization Theory and Applications
High Order Infeasible-Interior-Point Methods for Solving Sufficient Linear Complementarity Problems
Mathematics of Operations Research
Mathematics of Operations Research
Mathematics of Operations Research
Complexity Analysis of an Interior Cutting Plane Method for Convex Feasibility Problems
SIAM Journal on Optimization
SIAM Journal on Optimization
Primal-Dual Interior-Point Methods for Self-Scaled Cones
SIAM Journal on Optimization
Polynomial Convergence of a New Family of Primal-Dual Algorithms for Semidefinite Programming
SIAM Journal on Optimization
A Multiple-Cut Analytic Center Cutting Plane Method for Semidefinite Feasibility Problems
SIAM Journal on Optimization
SIAM Journal on Optimization
Primal--Dual Path-Following Algorithms for Semidefinite Programming
SIAM Journal on Optimization
SIAM Journal on Optimization
On the Nesterov--Todd Direction in Semidefinite Programming
SIAM Journal on Optimization
SIAM Journal on Optimization
An Analytic Center Cutting Plane Method for Semidefinite Feasibility Problems
Mathematics of Operations Research
Mathematical Programming: Series A and B
Error Bounds and Limiting Behavior of Weighted Paths Associated with the SDP Map X1/2SX1/2
SIAM Journal on Optimization
Asymptotic behavior of the central path for a special class of degenerate SDP problems
Mathematical Programming: Series A and B
A finite steps algorithm for solving convex feasibility problems
Journal of Global Optimization
Mathematical Programming: Series A and B
Analyticity of weighted central paths and error bounds for semidefinite programming
Mathematical Programming: Series A and B
Limiting behavior of the Alizadeh-Haeberly-Overton weighted paths in semidefinite programming
Optimization Methods & Software
Limiting behaviour and analyticity of weighted central paths in semidefinite programming
Optimization Methods & Software - The 22nd European Conference on Operational Research, 8-11 July 2007, Prague, Czech Republic
Optimization Methods & Software
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An interior point method (IPM) defines a search direction at each interior point of a region. These search directions form a direction field which in turn gives rise to a system of ordinary differential equations (ODEs). The solutions of the system of ODEs can be viewed as underlying paths in the interior of the region. In [C.-K. Sim and G. Zhao, Math. Program. Ser. A, 110 (2007), pp. 475-499], these off-central paths are shown to be well-defined analytic curves, and any of their accumulation points is a solution to a given monotone semidefinite linear complementarity problem (SDLCP). The study of these paths provides a way to understand how iterates generated by an interior point algorithm behave. In this paper, we give a sufficient condition using these off-central paths that guarantees superlinear convergence of a predictor-corrector path-following interior point algorithm for SDLCP using the Helmberg-Kojima-Monteiro (HKM) direction. This sufficient condition is implied by a currently known sufficient condition for superlinear convergence. Using this sufficient condition, we show that for any linear semidefinite feasibility problem, superlinear convergence using the interior point algorithm, with the HKM direction, can be achieved for a suitable starting point. We work under the assumption of strict complementarity.