Related papers: Generalised Mathematical Formulations for Non-Line…
Network slicing is a key technique in 5G and beyond for efficiently supporting diverse services. Many network slicing solutions rely on deep learning to manage complex and high-dimensional resource allocation problems. However, deep…
In this paper we present a Mixed Integer Nonlinear Programming model that we developed as part of a pilot study requested by the R&D company Metrolab in order to design tools for finding solutions for line planning and timetable situations…
The introduction of 5G networks has significantly advanced communication technology, offering faster speeds, lower latency, and greater capacity. This progress sets the stage for Beyond 5G (B5G) networks, which present new complexity and…
Quantum Computing offers a new paradigm for efficient computing and many AI applications could benefit from its potential boost in performance. However, the main limitation is the constraint to linear operations that hampers the…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
A current trend in networking and cloud computing is to provide compute resources at widely dispersed places; this is exemplified by developments such as Network Function Virtualisation. This paves the way for wide-area service deployments…
This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…
Based on the matrix expression of general nonlinear numerical analogues presented by the present author, this paper proposes a novel philosophy of nonlinear computation and analysis. The nonlinear problems are considered an ill-posed linear…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
The rapid growth in the number and variety of connected devices requires 5G wireless systems to cope with a very heterogeneous traffic mix. As a consequence, the use of a fixed TTI during transmission is not necessarily the most efficacious…
Designing networks with specified collective properties is useful in a variety of application areas, enabling the study of how given properties affect the behavior of network models, the downscaling of empirical networks to workable sizes,…
We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…
The principal innovative idea in this paper is to transform the original complex nonlinear modeling problem into a combination of linear problem and very simple nonlinear problems. The key step is the generalized linearization of nonlinear…
The field of optimization has gotten a lot of interest in recent years owing to significant advances in computer technology. Numerous issues in machine learning, economics, finance, geophysics, molecular modeling, computational systems…
We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the…
The linear model uses the space defined by the input to project the target or desired signal and find the optimal set of model parameters. When the problem is nonlinear, the adaption requires nonlinear models for good performance, but it…
It is well known that opportunistic scheduling algorithms are throughput optimal under dynamic channel and network conditions. However, these algorithms achieve a hypothetical rate region which does not take into account the overhead…
Modern networks support network slicing, which partitions physical infrastructure into virtual slices tailored to different service requirements (for example, high bandwidth or low latency). Optimally allocating users to slices is a…
The fifth-generation (5G) networks are expected to be able to satisfy users' different quality-of-service (QoS) requirements. Network slicing is a promising technology for 5G networks to provide services tailored for users' specific QoS…
In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the…