Related papers: Linear lexicographic optimization and preferential…
Airplane refueling problem is a nonlinear unconstrained optimization problem with $n!$ feasible solutions. Given a fleet of $n$ airplanes with mid-air refueling technique, the question is to find the best refueling policy to make the last…
The rapid advancement in large language models (LLMs) has brought forth a diverse range of models with varying capabilities that excel in different tasks and domains. However, selecting the optimal LLM for user queries often involves a…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
In this paper, we develop a new method for finding an optimal biddingstrategy in sequential auctions, using a dynamic programming technique. Theexisting method assumes that the utility of a user is represented in anadditive form. Thus, the…
We use the lexicographic order to define a hierarchy of primal and dual bounds on the optimum of a bounded integer program. These bounds are constructed using lex maximal and minimal feasible points taken under different permutations. Their…
In a sequential auction with multiple bidding agents, it is highly challenging to determine the ordering of the items to sell in order to maximize the revenue due to the fact that the autonomy and private information of the agents heavily…
Building on the previous work of Lee et al. and Ferdinand et al. on coded computation, we propose a sequential approximation framework for solving optimization problems in a distributed manner. In a distributed computation system, latency…
We introduce a general method for relaxing decision diagrams that allows one to bound job sequencing problems by solving a Lagrangian dual problem on a relaxed diagram. We also provide guidelines for identifying problems for which this…
We introduce a new approach for the numerical pricing of American options. The main idea is to choose a finite number of suitable excessive functions (randomly) and to find the smallest majorant of the gain function in the span of these…
It is introduced the using of generation lexicographical procedure for multicriteria decision-making problems.
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
In the development of industrial digital twins, the optimization problem of technological and business processes often arises. In many cases, this problem can be reduced to a large-scale linear programming (LP) problem. The article is…
The discrete Wasserstein barycenter problem is a minimum-cost mass transport problem for a set of discrete probability measures. Although an exact barycenter is computable through linear programming, the underlying linear program can be…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
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…
Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provides an overview of the recent development of first-order…
Periodic timetabling for public transportation networks is typically modelled as a Periodic Event Scheduling Problem (PESP). Solving instances of the benchmark library PESPlib to optimality continues to pose a challenge. As a further…