Related papers: Tropical optimization techniques in multi-criteria…

In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…

The Analytic Hierarchy Process (AHP) is a procedure for establishing priorities in multi-criteria decision making problems. Here we discuss the Logarithmic Least Squares (LLS) method for the AHP and group-AHP, which provides an exact and…

We give a framework for constructing generically optimal homotopies for parametrized polynomial systems from tropical data. Here, generically optimal means that the number of paths tracked is equal to the generic number of solutions. We…

We initiate the systematic study of decision-theoretic metrics in the design and analysis of algorithms with machine-learned predictions. We introduce approaches based on both deterministic measures such as distance-based evaluation, that…

The problem of low rank approximation is ubiquitous in science. Traditionally this problem is solved in unitary invariant norms such as Frobenius or spectral norm due to existence of efficient methods for building approximations. However,…

This paper introduces Bayesian frameworks for tackling various aspects of multi-criteria decision-making (MCDM) problems, leveraging a probabilistic interpretation of MCDM methods and challenges. By harnessing the flexibility of Bayesian…

Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise…

Tropical cyclones present a serious threat to many coastal communities around the world. Many numerical weather prediction models provide deterministic forecasts with limited measures of their forecast uncertainty. Standard postprocessing…

Hierarchical classification addresses the problem of classifying items into a hierarchy of classes. An important issue in hierarchical classification is the evaluation of different classification algorithms, which is complicated by the…

We consider discrete linear Chebyshev approximation problems in which the unknown parameters of linear function are fitted by minimizing the maximum absolute deviation of errors. Such problems find application in the solution of…

This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…

In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…

In many operations management problems, we need to make decisions sequentially to minimize the cost while satisfying certain constraints. One modeling approach to study such problems is constrained Markov decision process (CMDP). When…

We provide a framework for speeding up algorithms for time-bounded reachability analysis of continuous-time Markov decision processes. The principle is to find a small, but almost equivalent subsystem of the original system and only analyse…

We introduce a method for explaining the results of various linear and hierarchical multi-criteria decision-making (MCDM) techniques such as WSM and AHP. The two key ideas are (A) to maintain a fine-grained representation of the values…

When optimizing real-time systems, designers often face a challenging problem where the schedulability constraints are non-convex, non-continuous, or lack an analytical form to understand their properties. Although the optimization…

Multi-objective optimization aims at finding trade-off solutions to conflicting objectives. These constitute the Pareto optimal set. In the context of expensive-to-evaluate functions, it is impossible and often non-informative to look for…

In certain real-world optimization scenarios, practitioners are not interested in solving multiple problems but rather in finding the best solution to a single, specific problem. When the computational budget is large relative to the cost…

Algorithmic fairness seeks to identify and correct sources of bias in machine learning algorithms. Confoundingly, ensuring fairness often comes at the cost of accuracy. We provide formal tools in this work for reconciling this fundamental…

Pairwise comparison methods, such as Fuzzy Preference Relations and Saaty's Multiplicative Preference Relations, are widely used to model expert judgments in multi-criteria decision-making. However, their application is limited by the high…