Segment routing, a modern protocol enhancing traffic engineering, introduces flexibility by
enabling traffic to take detours. This talk tackles the challenge of optimizing routing in the face of
uncertain traffic distribution. Unlike traditional methods relying on a single traffic matrix, our approach
considers an infinite set of matrices defined by linear constraints. Our goal is to optimize routing under the
worst-case scenario within this set. Through innovative formulations, our results showcase a substantial
speed improvement in optimization compared to traditional methods, offering an efficient alternative to
exploring all extreme points in the matrix set.

This work presents a novel approach for jointly optimizing inter- and intra-frequency events in multi-carrier scenarios with user equipment (UE) mobility for radio networks. We propose leveraging sequential learning techniques to learn the optimal group of continuous global handovers (HOs). Our method includes performance evaluation for UE traffic mix with various Quality-of-Experience (QoE) requirements and different load/mobility patterns. Furthermore, we select an appropriate global multi-objective function to optimize performance metrics such as the number of HOs, ping-pong effect, inter-carrier load, etc for a given input traffic mix.

The Augmented Lagrangian Method (ALM) is one of the most common approaches for solving linear and nonlinear constrained problems. However, for nonconvex objectives, the handling of nonlinear inequality constraints remains challenging. In this paper, we propose a stochastic ALM with Backtracking Line Search that performs on a subset (mini-batch) of randomly selected points for the solving of nonconvex problems. The considered class of problems include both nonlinear equality and inequality constraints. Together with the formal proof of the convergence properties (in expectation) of the proposed algorithm and its computational complexity, the performance of the proposed algorithm are then numerically compared against both exact and inexact state-of-the-art ALM methods. Further, we apply the proposed stochastic ALM method to solve a multi-constrained network design problem. We perform extensive numerical executions on a set of instances extracted from SNDlib to study its behavior and performance as well as potential improvement of this method. Analysis and comparison of the results against those obtained by extending to nonlinear constraints methods developed for the approximation of separable nonconvex optimization programs are then provided.