In this paper, we investigate a new primal-dual long-step interior point algorithm for linear optimization. Based on the step-size, interior point algorithms can be divided into two main groups, short-step and long-step methods. In practice, long-step variants perform better, but usually, a...

In this paper, we introduce a general long-step algorithmic framework for solving linear programming problems based on the algebraically equivalent transformation technique proposed by Darvay. The main characteristics of the proposed general interior point algorithm are based on the long-step...

We present an interior-point algorithmic framework for P_* (κ)-Linear Complementarity Problems that is based on a barrier function which is defined by a new class of univariate kernel functions called Standard Kernel Functions (SKFs). A unified, comprehensive complexity analysis of the generic...

In this paper, we revisit the main principles for constructing polynomial-time primal-dual interior-point algorithms (IPAs). Starting from the break-through paper by Gonzaga (1989), their development was related to the barrier methods, where the objective function was added to the barrier for...

In this paper, we suggest a new interior-point method for linear optimization, based on the idea of Parabolic Target Space. Our method can start at any strictly feasible primal-dual pair and go directly towards a solution by a predictor-corrector scheme. Each iteration needs inversion of a...