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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…
This paper deals with the maximum independent set (M.I.S.) problem, also known as the stable set problem. The basic mathematical programming model that captures this problem is an Integer Program (I.P.) with zero-one variables $x_j$ and…
Estimating the absolute orientation of a local system relative to a global navigation satellite system (GNSS) reference often suffers from local minima and high dependency on satellite availability. Existing methods for this alignment task…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
This paper proposes a novel approach to solving nonlinear programming problems using a sharp augmented Lagrangian method with a smoothing technique. Traditional sharp augmented Lagrangian methods are known for their effectiveness but are…
In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…
Model reduction, which aims to learn a simpler model of the original mixed integer linear programming (MILP), can solve large-scale MILP problems much faster. Most existing model reduction methods are based on variable reduction, which…
Low Earth orbit (LEO) mega-constellations greatly extend the coverage and resilience of future wireless systems. Within the mega-constellations, laser inter-satellite links (LISLs) enable high-capacity, long-range connectivity. Existing…
This paper studies the Graph-Connected Clique-Partitioning Problem (GCCP), a clustering optimization model in which units are characterized by both individual and relational data. This problem, introduced by Benati et al. (2017) under the…
The efficient allocation of human resources is a critical concern in software development and other industries. This paper introduces a rigorous mathematical methodology for task assignment, employing Mixed Integer Linear Programming (MILP)…
Recent theoretical developments in astronomical aperture synthesis have revealed the existence of integer-ambiguity problems. Those problems, which appear in the self-calibration procedures of radio imaging, have been shown to be similar to…
We study stochastic mixed integer programs with both first-stage and recourse decisions involving mixed integer variables. A new family of Lagrangian cuts, termed ``ReLU Lagrangian cuts," is introduced by reformulating the nonanticipativity…
The main focus of the work presented in this thesis is to develop an optimal control based formation flying control strategy for high precision formation flying of small satellites that have restricted computation and storage capacity.…
For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods sequentially minimize a Lagrangian function subject to linearized constraints. These methods converge rapidly near a solution but may not be…
With the growth of complexity and extent, large scale interconnected network systems, e.g. transportation networks or infrastructure networks, become more vulnerable towards external disruptions. Hence, managing potential disruptive events…
We propose an extended variant of the reformulation and decomposition algorithm for solving a special class of mixed-integer bilevel linear programs (MIBLPs) where continuous and integer variables are involved in both upper- and lower-level…
We introduce the Hierarchical Seating Allocation Problem (HSAP) which addresses the optimal assignment of hierarchically structured organizational teams to physical seating arrangements on a floor plan. This problem is driven by the…
In this paper we address the challenge of designing optimal domestic renewable energy systems under multiple sources of uncertainty appearing at different time scales. Long-term uncertainties, such as investment and maintenance costs of…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We study the problem of computing an optimal large language model (LLM) policy for the constrained alignment problem, where the goal is to maximize a primary reward objective while satisfying constraints on secondary utilities. Despite the…