A full Nesterov-Todd step primal-dual path-following interior-point algorithm for semidefinite linear complementarity problems

Abstract

In this paper, a feasible primal-dual path-following interior-point algorithm for monotone semidefinite linear complementarity problems is proposed. At each iteration, the algorithm uses only full Nesterov-Todd feasible steps for tracing approximately the central-path and getting an approximated solution of this problem. Under a new appropriate choices of the threshold τ which defines the size of the neighborhood of the central-path and of the update barrier parameter θ, we show that the algorithm is well-defined and enjoys the locally quadratically convergence. Moreover, we prove that the short-step algorithm deserves the best known iteration bound, namely, O(√ n log n). Finally, some numerical results are reported to show the practical performance of the algorithm.

Role of New Kernel Function in Complexity Analysis of an Interior Point Algorithm for Semi definite Linear Complementarity Problem

“…The first example is the monotone SDLCP defined by two sided multiplicative linear transformation [1] . The second is monotone SDLCP which is equivalent to the symmetric semidefinite least squares(SDLS)problem and the third one is reformulated from nonsymmetric semidefinite least squares(NS-SDLS)problem [10], in the second and third example, L is Lyaponov linear transformation.…”

“…These methods are based on the kernel functions for determining new search directions and new proximity functions for analyzing the complexity of these algorithms, thus we have shown the important role of the kernel function in generating a new design of primal-dual interior point algorithm. Also these methods are introduced by Bai et al [2], and Elghami [4] for (LO) and (SDO) and extended by many authors for different problems in mathematical programming [1], [3], [5], [8], [10]. The polynomial complexity of large update primal-dual algorithms is improved in contrast with the classical complexity given by logarithmic barrier functions by using this new form.…”