arXiv subjects

Petra Renáta Rigó

Publications and source records attributed to Petra Renáta Rigó.

2 recordsLinked to original sources

arXiv2026

Multiconic Optimization for Symmetric Cones and Hyperbolic Coupling

We develop a new interior-point algorithm for solving multiconic optimization problems using the parabolic target space approach. The feasible cone in these problems is composed as a direct product of many small-dimensional cones. Our approach is based on a new concept, called the hyperbolic coupling. This provides a new framework that has an advantage of interdependent pairs of primal-dual variables. In this way, their behaviour is much more controllable. We justify all main steps in the complexity analysis of the algorithm and prove that the overall complexity of solving this type of large-scale nonlinear problems by our algorithm is comparable with the best known complexity for solving linear programming problems of the same dimension.

math.OC↗

arXiv2025

Interior-Point Algorithms for Monotone Linear Complementarity Problem Based on Different Predictor Directions

In this paper, we introduce two parabolic target-space interior-point algorithms for solving monotone linear complementarity problems. The first algorithm is based on a universal tangent direction, which has been recently proposed for linear optimization problems. We prove that this method has the best known worst-case complexity bound. We extend onto LCP its auto-correcting version, and prove its local quadratic convergence under a non-degeneracy assumption. In our numerical experiments, we compare the new algorithms with a general method, recently developed for weighted monotone linear complementarity problems.

math.OC↗