This paper introduces a generalized isotonic optimization framework over an arborescence graph, where each node incurs state-dependent convex costs and a fixed cost upon strict increases. We begin with the special case in which the arborescence is a path and develop a dynamic programming (DP) algorithm with an initial complexity of $O(n^3)$, which we improve … Read more
As countries seek to decarbonize their energy systems, green hydrogen has emerged as a promising energy carrier. This paper studies the production of green hydrogen from offshore wind in the Dutch North Sea, with particular emphasis on understanding how system design decisions and uncertain parameters affect key performance indicators. The analysis builds on a detailed … Read more
Multiobjective optimization is widely used in applications for modeling and solving complex decision-making problems. To help resolve computational and cognitive difficulties associated with problems which have more than three or four objectives, we propose a decomposition and coordination methodology to support decision making for large multiobjective optimization problems (MOPs) with global, quasi-global, and local variables. … Read more
We study a generalization of the classical discrete-time, Linear-Quadratic-Gaussian (LQG) control problem where the noise distributions affecting the states and observations are unknown and chosen adversarially from divergence-based ambiguity sets centered around a known nominal distribution. For a finite horizon model with Gaussian nominal noise and a structural assumption on the divergence that is satisfied … Read more
We study a two-player zero-sum inspection game with incomplete information, where an inspector deploys resources to maximize the expected damage value of detected illegal items hidden by an adversary across capacitated locations. Inspection and illegal resources differ in their detection capabilities and damage values. Both players face uncertainty regarding each other’s available resources, modeled via … Read more
Recognizing the strength of parametric optimization to model uncertainty, we extend the classical linear programming duality theory to a parametric setting. For linear programs with parameters in general locations, we prove parametric weak and strong duality theorems and parametric complementary slackness theorems. ArticleDownload
Collection point networks are rapidly expanding as delivery companies and public authorities promote their implementation to consolidate deliveries and reduce urban congestion. However, rather than catering to public interest by maximizing accessibility, the placement of collection points remains primarily driven by competition among delivery companies, which seek to maximize their market share. This paper thus … Read more
We present MultiObjectiveAlgorithms.jl, an open-source Julia library for solving multi-objective optimization problems written in JuMP. MultiObjectiveAlgorithms.jl implements a number of different solution algorithms, which all rely on an iterative scalarization of the problem from a multi-objective optimization problem to a sequence of single-objective subproblems. As part of this work, we extended JuMP to support vector-valued … Read more
As inherently transparent models, classification trees play a central role in interpretable machine learning by providing easily traceable decision paths that allow users to understand how input features contribute to specific predictions. In this work, we introduce a new class of interpretable binary classification models, named Pareto-optimal trees, which aim at combining the complementary strengths … Read more
Optimization problems that involve multiple, conflicting criteria lead to a set of efficient solutions, and when there are discrete decisions, some solutions may be unsupported. Applications where it is difficult to estimate the parameters for criteria motivate inverse optimization techniques. We provide a theoretical analysis of the set of (unknown) objective parameters which lead to … Read more