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Optimization is a key task in a number of applications. When the set of feasible solutions under consideration is of combinatorial nature and described in an implicit way as a set of constraints, optimization is typically NP-hard.…
Large Language Models (LLMs) have shown remarkable capabilities in solving various programming tasks, such as code generation. However, their potential for code optimization, particularly in performance enhancement, remains largely…
We take an axiomatic approach to study redistribution problems when agents report income and needs. We formalize axioms reflecting ethical and operational principles such as additivity, impartiality and individual rationality. Different…
We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…
We propose a parametric specification of the probability of tax penalisation faced by a taxpayer, based on the amount of deduction chosen by her to reduce total taxation. Comparative analyses lead to a closed-form solution for the optimum…
We introduce a highly stylized, yet non trivial model of the economy, with a public and private sector coupled through a wealth tax and a redistribution policy. The model can be fully solved analytically, and allows one to address the…
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…
Chance-constrained programming (CCP) is one of the most difficult classes of optimization problems that has attracted the attention of researchers since the 1950s. In this survey, we focus on cases when only a limited information on the…
Due to the ever-increasing complexity of income tax laws in the United States, the number of US taxpayers filing their taxes using tax preparation software (henceforth, tax software) continues to increase. According to the U.S. Internal…
We describe a convex programming approach to the calculation of lower bounds on the minimum cost of constrained decentralized control problems with nonclassical information structures. The class of problems we consider entail the…
In this brief, we consider the constrained optimization problem underpinning model predictive control (MPC). We show that this problem can be decomposed into an unconstrained optimization problem with the same cost function as the original…
Real-world experiments involve batched & delayed feedback, non-stationarity, multiple objectives & constraints, and (often some) personalization. Tailoring adaptive methods to address these challenges on a per-problem basis is infeasible,…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
Models based on approximation capabilities have recently been studied in the context of Optimal Recovery. These models, however, are not compatible with overparametrization, since model- and data-consistent functions could then be…
The continuous-time analysis of existing iterative algorithms for optimization has a long history. This work proposes a novel continuous-time control-theoretic framework for equality-constrained optimization. The key idea is to design a…
This paper draws on diverse areas of computer science to develop a unified view of computation: (1) Optimization in operations research, where a numerical objective function is maximized under constraints, is generalized from the numerical…
We study revenue maximization in a buyer-seller setting where the seller has a single object and the buyer has both a private valuation and a private budget. Private budgets complicate the classic single-product monopoly problem, making…
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
In the so-called ``fair'' models of peer-to-peer wealth exchanges, economic inequality tends to reach its maximum value asymptotically. This global trend is evident as the richest continuously accumulate a larger share of wealth at the…