We propose new short-step interior-point algorithms (IPAs) for solving P_* (κ)-linear complementarity problems (LCPs). In order to define the search directions we use the algebraic equivalent transformation technique (AET) of the system which characterizes the central path. A novelty of the...

This brief note presents a personal recollection of the early history of EUROpt, the Continuous Optimization Working Group of EURO. This historical note details the events that happened before the formation of EUROpt Working Group and the first five years of its existence. During the early years...

In this paper we introduce a new predictor-corrector interior-point algorithm for solving P_* (κ)-linear complementarity problems. For the determination of search directions we use the algebraically equivalent transformation (AET) technique. In this method we apply the function φ(t)=t^2-t+√t...

We propose new short-step interior-point algorithms (IPAs) for solving P_*(\kappa ) P ∗ ( κ ) -linear complementarity problems (LCPs). In order to define the search directions, we use the algebraic equivalent transformation (AET) technique of the system describing the central path. A novelty...

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...