a path following interior-point algorithm for semidefinite optimization problem based on new kernel function

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• A path following interior-point algorithm for semidefinite optimization problem based on new kernel function

  Article2016Journal of Mathematical ModelingEl Amir Djeffal, Lakhdar Djeffal

  In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual inte

• Superlinear Convergence of an Infeasible Predictor-Corrector Path-Following Interior Point Algorithm for a Semidefinite Linear Complementarity Problem Using the Helmberg--Kojima--Monteiro Direction

  Scholarly record2011SIAM Journal on OptimizationChee-Khian Sim

  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 underl

• A new class of large neighborhood path - following interior point algorithms for semidefinite optimization with O ( √ n log Tr ( X 0 S 0 ) 2 ) iteration complexity

  Scholarly record2008Yang Li, Tamás Terlaky

  In this paper, we extend the Ai-Zhang direction to the class of semidefinite optimization problems. We define a new wide neighborhood N (τ1, τ2, η) and, as usual, we utilize symmetric directions by scaling the Newton equation with special matrices. After defining the “positive pa

• A New Class of Large Neighborhood Path-Following Interior Point Algorithms for Semidefinite Optimization with O(√n log (Tr(X0S0)/ε)) Iteration Complexity

  Scholarly record2010SIAM Journal on OptimizationYang Li, Tamás Terlaky

  In this paper, we extend the Ai-Zhang direction to the class of semidefinite optimization problems. We define a new wide neighborhood N (τ1, τ2, η) and, as usual but with a small change, we make use of the scaled Newton equations for symmetric search directions. After defining th

• A unified analysis for a class of long-step primal-dual path-following interior-point algorithms for semidefinite programming

  Scholarly record1998Math. Program.Renato D. C. Monteiro, Yin Zhang

  We present a unified analysis for a class of long-step primal-dual path-following algorithms for semidefinite programming whose search directions are obtained through linearization of the symmetrized equation of the central path Hp(XS) -[PXSP -~ + (PXSP 1)TI/2 = #I, introduced by

• A polynomial path-following interior point algorithm for general linear complementarity problems

  Scholarly record2010J. Global OptimizationTibor Illés, Marianna Nagy, Tamás Terlaky

  Linear Complementarity Problems (LC Ps) belong to the class of NP-complete problems. Therefore we cannot expect a polynomial time solution method for LC Ps without requiring some special property of the coefficient matrix. Our aim is to construct interior point algorithms which,