Asymptotic behavior of helmberg-kojima-Monteiro (HKM) paths in interior-point methods for monotone semidefinite linear complementarity problems: General theory

DOI10.1007/s10957-007-9280-3zbMath1144.90494OpenAlexW2000113695WikidataQ58028372 ScholiaQ58028372MaRDI QIDQ927226

Chee-Khian Sim, Gongyun Zhao

Publication date: 4 June 2008

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10957-007-9280-3

zbMATH Keywords

Ordinary differential equationsAnalyticityHKM directionOff-central pathsSemidefinite linear complementarity problems

Mathematics Subject Classification ID

Semidefinite programming (90C22) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Interior-point methods (90C51)

Related Items

Asymptotic behavior of underlying NT paths in interior point methods for monotone semidefinite linear complementarity problems ⋮ The Convergent Generalized Central Paths for Linearly Constrained Convex Programming ⋮ Interior point method on semi-definite linear complementarity problems using the Nesterov-Todd (NT) search direction: polynomial complexity and local convergence ⋮ A strategy of global convergence for the affine scaling algorithm for convex semidefinite programming ⋮ Complementarity Problems Over Symmetric Cones: A Survey of Recent Developments in Several Aspects ⋮ On the analyticity of underlying HKM paths for monotone semidefinite linear complementarity problems

Cites Work

• Underlying paths in interior point methods for the monotone semidefinite linear complementarity problem
• On the complexity of following the central path of linear programs by linear extrapolation. II
• Estimating the complexity of a class of path-following methods for solving linear programs by curvature integrals
• On quadratic and \(O(\sqrt{n}L)\) convergence of a predictor-corrector algorithm for LCP
• A primal-dual interior point method whose running time depends only on the constraint matrix
• On the rate of local convergence of high-order-infeasible-path-following algorithms for \(P_*\)-linear complementarity problems
• Analysis of infeasible-interior-point paths arising with semidefinite linear complementarity problems
• The curvature integral and the complexity of linear complementarity problems
• A quadratically convergent \(O(\sqrt n\;L)\)-iteration algorithm for linear programming
• Asymptotic behavior of the central path for a special class of degenerate SDP problems
• High Order Infeasible-Interior-Point Methods for Solving Sufficient Linear Complementarity Problems
• Superlinear Convergence of an Algorithm for Monotone Linear Complementarity Problems, When No Strictly Complementary Solution Exists
• Quadratic Convergence in a Primal-Dual Method
• The Nonlinear Geometry of Linear Programming. III Projective Legendre Transform Coordinates and Hilbert Geometry
• The Nonlinear Geometry of Linear Programming. I Affine and Projective Scaling Trajectories
• The Nonlinear Geometry of Linear Programming. II Legendre Transform Coordinates and Central Trajectories
• On the Nesterov--Todd Direction in Semidefinite Programming
• On Extending Some Primal--Dual Interior-Point Algorithms From Linear Programming to Semidefinite Programming
• On the Convergence of the Central Path in Semidefinite Optimization
• On the Relationship Between the Curvature Integral and the Complexity of Path-Following Methods in Linear Programming
• Error Bounds and Limiting Behavior of Weighted Paths Associated with the SDP Map X1/2SX1/2
• Limiting behavior of the Alizadeh–Haeberly–Overton weighted paths in semidefinite programming

This page was built for publication: Asymptotic behavior of helmberg-kojima-Monteiro (HKM) paths in interior-point methods for monotone semidefinite linear complementarity problems: General theory