A corrector–predictor interior-point method with new search direction for linear optimization

A New Infeasible Interior-Point Algorithm with Full Nesterov-Todd Step for Semi-Definite Optimization

  We present a new full Nesterov and Todd step infeasible interior-point algorithm for semi-definite optimization. The algorithm decreases the duality gap and the feasibility residuals at the same rate. In the algorithm, we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Every main iteration of the algorithm consists of a feasibili...

A New Interior Point Method for Linear Complementarity Problem

named interior points set of the LCP (M, q) must be nonempty. The aim of this paper is to show that the LCP (M, q) is completely equivalent to a convex quadratic programming problem (CQPP ) under linear constraints. To solve the second problem, we propose an iterative method of interior points which converge in polynomial time to the exact solution; this convergence requires at most o(n0,5L) it...

Interior-point method for non-linear non-convex optimization

A primal-dual interior-point method for linear optimization based on a new proximity function

In this paper we present a generic primal-dual interior-point algorithm for linear optimization in which the search direction depends on a univariate kernel function which is also used as proximity measure in the analysis of the algorithm. We present some powerful tools for the analysis of the algorithm under the assumption that the kernel function satisfies three easy to check and mild conditi...

Interior Point Methods for Linear Optimization: Exercises