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Abstract
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We present an infeasible interior-point algorithm for symmetric linear complementarity
problem based on modified Nesterov–Todd directions by using
Euclidean Jordan algebras. The algorithm decreases the duality gap and the
feasibility residual at the same rate. In this algorithm, we construct strictly feasible
iterates for a sequence of perturbations of the given problem. Each main iteration
of the algorithm consists of a feasibility step and a number of centring steps. The
starting point in the first iteration is strictly feasible for a perturbed problem. The
feasibility steps lead to a strictly feasible iterate for the next perturbed problem.
By using centring steps for the new perturbed problem, a strictly feasible iterate is
obtained to be close to the central path of the new perturbed problem. Furthermore,
giving a complexity analysis of the algorithm, we derive the currently best-known
iteration bound for infeasible interior-point methods.
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