## Adaptive Large Neighborhood Self-Regular Predictor-Corrector IPMs for LO

It is known that predictor-corrector methods in a large neighborhood of the central path are among the most efficient interior point methods (IPMs) for linear optimization (LO) problems. The best iteration bound based on the classical logarithmic barrier function is $O\left(n\log{\frac{n}{\epsilon}}\right)$. In this paper we propose a family of self-regular proximity based predictor-corrector (SR-PC) IPM … Read more

## An Adaptive Self-Regular Proximity Based Large-Update IPM for LO

Primal-Dual Interior-Point Methods (IPMs) have shown their power in solving large classes of optimization problems. However, there is still a gap between the practical behavior of these algorithms and their theoretical worst-case complexity results with respect to the update strategies of the duality gap parameter in the algorithm. The so-called small-update IPMs enjoy the best … Read more

## The Complexity of Self-Regular Proximity Based Infeasible IPMs

Primal-Dual Interior-Point Methods (IPMs) have shown their power in solving large classes of optimization problems. In this paper a self-regular proximity based Infeasible Interior Point Method (IIPM) is proposed for linear optimization problems. First we mention some interesting perties of a specific self-regular proximity function, studied recently by Peng and Terlaky, and use it to … Read more

## A predictor-corrector algorithm for linear optimization based on a specific self-regular proximity function

It is well known that the so-called first-order predictor-corrector methods working in a large neighborhood of the central path are among the most efficient interior-point methods (IPMs) for linear optimization (LO) problems. However, the best known iteration complexity of this type of methods is $O\br{n \log\frac{(x^0)^Ts^0}{\varepsilon}}$. It is of interests to investigate whether the complexity … Read more