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Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…
In this thesis, we settle the computational complexity of some fundamental questions in polynomial optimization. These include the questions of (i) finding a local minimum, (ii) testing local minimality of a point, and (iii) deciding…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
In beyond 5G and 6G network scenarios, the use of satellites has been actively discussed for extending target monitoring areas, even for extreme circumstances, where the monitoring functionalities can be realized due to the usage of…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
With the increasing attention to the integrated satellite-terrestrial networks (ISTNs), the satellite gateway placement problem becomes of paramount importance. The resulting network performance may vary depending on the different design…
In a wireless system with a large number of distributed nodes, the quality of communication can be greatly improved by pooling the nodes to perform joint transmission/reception. In this paper, we consider the problem of optimally selecting…
To overcome the limited on-board battery issue of nominal airborne base stations (ABSs), we are exploring the use of robotic airborne base station (RABS) with energy neutral grasping end-effectors that are able to autonomously perch at tall…
Low Earth orbit (LEO) satellites has brought about significant improvements in wireless communications, characterized by low latency and reduced transmission loss compared to geostationary orbit (GSO) satellites. Ultra-dense LEO satellites…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
We propose integer-programming formulations for an optimal safety-landing site (SLS) location problem that arises in the design of urban air-transportation networks. We first develop a set-cover based approach for the case where the…
Earth imaging satellites are a crucial part of our everyday lives that enable global tracking of industrial activities. Use cases span many applications, from weather forecasting to digital maps, carbon footprint tracking, and vegetation…
We consider the facility location problem in the one-dimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the…
SDN-enabled Integrated satellite-terrestrial networks (ISTNs), can provide several advantages including global seamless coverage, high reliability, low latency, etc. and can be a key enabler towards next generation networks. To deal with…
We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…
Our research deals with the optimization version of the set partition problem, where the objective is to minimize the absolute difference between the sums of the two disjoint partitions. Although this problem is known to be NP-hard and…
We perform structural and algorithmic studies of significantly generalized versions of the optimal perimeter guarding (OPG) problem. As compared with the original OPG where robots are uniform, in this paper, many mobile robots with…
We consider the state-minimisation problem for weighted and probabilistic automata. We provide a numerically stable polynomial-time minimisation algorithm for weighted automata, with guaranteed bounds on the numerical error when run with…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…