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Interior-Point Methods for the Monotone Semidefinite Linear Complementarity Problem in Symmetric Matrices
TLDR
The aim of this paper is to establish a theoretical basis of interior-point methods with the use of Newton directions toward the central trajectory for the monotone SDLCP.
Local convergence of predictor—corrector infeasible-interior-point algorithms for SDPs and SDLCPs
TLDR
An example of an SDP exhibits a substantial difficulty in proving the superlinear convergence of a direct extension of the Mizuno—Todd—Ye type predictor—corrector primal-dual interior-point method, and suggests that the authors need to force the generated sequence to converge to a solution tangentially to the central path (or trajectory).
A Predictor-Corrector Interior-Point Algorithm for the Semidefinite Linear Complementarity Problem Using the Alizadeh-Haeberly-Overton Search Direction
This paper proposes a globally convergent predictor-corrector infeasible-interior-point algorithm for the monotone semidefinite linear complementarity problem using the Alizadeh--Haeberly--Overton
Search directions in the SDP and the monotone SDLCP: generalization and inexact computation
TLDR
A predictor-corrector infeasible-interior-point method is presented to provide a theoretical basis for inexact computation of directions in primal-dual interior-point methods for the SDP.
Existence and Uniqueness of Search Directions in Interior-Point Algorithms for the SDP and the Monotone SDLCP
TLDR
This observation provides a unified geometric view over the existence ofVarious search directions used in interior-point algorithms for the semidefinite program (SDP) and the monotone semideFinite linear complementarity problem (SDLCP).
Existence of Search Directions in Interior-Point Algorithms for the SDP and the Monotone SDLCP
Various search directions used in interior-point-algorithms for the SDP (semidefinite program) and the monotone SDLCP (semide nite linear complementarity problem) are characterized by the
Horizontal and vertical decomposition in interior point methods for linear programs
Corresponding to the linear program Maximize cx subject to Ax a Bx b x we introduce two functions in the penalty parameter t and the Lagrange relaxation parameter vector w f p t w maxfcx w Ax a t n X
A note on the Nesterov-Todd and the Kojima-Shindoh-hara search directions in semidefinite programming
This short note shows that the Nesterov-Todd search direction used in primal-dual interior-point methods for semidefinite programs belongs to the family of search directions proposed by Kojima,
REDUCTION OF MONOTONE LINEAR COMPLEMENTARITY PROBLEMS OVER CONES TO LINEAR PROGRAMS OVER CONES
Dedicated to Hoang Tuy on the occasion of his seventieth birthday Abstract. This short note presents a constructive way of reducing monotone LCPs (linear complementarity problems) over cones to LPs
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