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Multi-band transmission is a promising technical direction for spectrum and capacity expansion of existing optical networks. Due to the increase in the number of usable wavelengths in multi-band optical networks, the complexity of resource…

Crew Pairing Optimization (CPO) is critical for an airlines' business viability, given that the crew operating cost is second only to the fuel cost. CPO aims at generating a set of flight sequences (crew pairings) to cover all scheduled…

In the day-ahead energy market, the offering strategy of distributed energy resource (DER) aggregators must be submitted before the uncertainty realization in the form of price-quantity pairs. This work addresses the day-ahead offering…

This work investigates a variant of the conjugate gradient (CG) method and embeds it into the context of high-order finite-element schemes with fast matrix-free operator evaluation and cheap preconditioners like the matrix diagonal. Relying…

The tabular form constitutes the standard way of representing data in relational database systems and spreadsheets. But, similarly to other forms, tabular data suffers from class imbalance, a problem that causes serious performance…

Capacity sharing networks are typical heterogeneous communication networks widely applied in information and communications technology (ICT) field. In such networks, resources like bandwidth, spectrum, computation and storage are shared…

Decision trees are highly interpretable models for solving classification problems in machine learning (ML). The standard ML algorithms for training decision trees are fast but generate suboptimal trees in terms of accuracy. Other discrete…

In this study, the periodic train timetabling problem is formulated using a time-space graph formulation. Three solution methods are proposed and compared where solutions are built by what we define as a dive-and-cut-and-price procedure. An…

The template-based method is one of the most successful approaches to algebraic invariant synthesis. In this method, an algorithm designates a template polynomial p over program variables, generates constraints for p=0 to be an invariant,…

Online advertising has become a core revenue driver for the internet industry, with ad auctions playing a crucial role in ensuring platform revenue and advertiser incentives. Traditional auction mechanisms, like GSP, rely on the independent…

Stochastic programming provides a natural framework for modeling sequential optimization problems under uncertainty; however, the efficient solution of large-scale multistage stochastic programs remains a challenge, especially in the…

We develop a general framework for MAP estimation in discrete and Gaussian graphical models using Lagrangian relaxation techniques. The key idea is to reformulate an intractable estimation problem as one defined on a more tractable graph,…

The minimum sum-of-squares clustering problem (MSSC), also known as $k$-means clustering, refers to the problem of partitioning $n$ data points into $k$ clusters, with the objective of minimizing the total sum of squared Euclidean distances…

In this paper, we propose an effective search procedure that interleaves two steps: subproblem generation and subproblem solution. We mainly focus on the first part. It consists of a variable domain value ranking based on reduced costs.…

We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by…

In certain electricity markets, because of non-convexities that arise from their operating characteristics, generators that follow the independent system operator's (ISO's) decisions may fail to recover their cost through sales of energy at…

The rapid advancement of large language models (LLMs) such as GPT-3, PaLM, and Llama has significantly transformed natural language processing, showcasing remarkable capabilities in understanding and generating language. However, a…

We develop a simple yet efficient Lagrangian method for computing equilibrium prices in a mean-field game price-formation model. We prove that equilibrium prices are optimal in terms of a suitable criterion and derive a primal-dual…

Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…

Gradient Descent (GD) and Conjugate Gradient (CG) methods are among the most effective iterative algorithms for solving unconstrained optimization problems, particularly in machine learning and statistical modeling, where they are employed…