Related papers: An Optimization Perspective on the Monotonicity of…
Monotonicity and convex analysis arise naturally in the framework of multi-marginal optimal transport theory. However, a comprehensive multi-marginal monotonicity and convex analysis theory is still missing. To this end we study extensions…
We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…
While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…
In optimal transport, quadratic regularization is a sparse alternative to entropic regularization: the solution measure tends to have small support. Computational experience suggests that the support decreases monotonically to the…
A basic requirement for a mathematical model is often that its solution (output) shouldn't change much if the model's parameters (input) are perturbed. This is important because the exact values of parameters may not be known and one would…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
Matching mechanisms play a central role in operations management across diverse fields including education, healthcare, and online platforms. However, experimentally comparing a new matching algorithm against a status quo presents some…
In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the…
Electric machine design optimization is a computationally expensive multi-objective optimization problem. While the objectives require time-consuming finite element analysis, optimization constraints can often be based on mathematical…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
In this paper, the preliminary design of a space mission is approached introducing uncertainties on the design parameters and formulating the resulting reliable design problem as a multiobjective optimization problem. Uncertainties are…
Empirical analysis serves as an important complement to theoretical analysis for studying practical Bayesian optimization. Often empirical insights expose strengths and weaknesses inaccessible to theoretical analysis. We define two metrics…
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…
The Metropolis process (MP) and Simulated Annealing (SA) are stochastic local search heuristics that are often used in solving combinatorial optimization problems. Despite significant interest, there are very few theoretical results…
We use techniques originating from the subdiscipline of mathematical logic called `proof mining' to provide rates of metastability and - under a metric regularity assumption - rates of convergence for a subgradient-type algorithm solving…
Often times, individuals working together as a team can solve hard problems beyond the capability of any individual in the team. Cooperative optimization is a newly proposed general method for attacking hard optimization problems inspired…
Extremal Optimization, a recently introduced meta-heuristic for hard optimization problems, is analyzed on a simple model of jamming. The model is motivated first by the problem of finding lowest energy configurations for a disordered spin…
Multicriteria adjustable robust optimization (MARO) problems arise in a wide variety of practical settings, for example, in the design of a building's energy supply. However, no general approaches, neither for the characterization of…
An analyst observes an agent take a sequence of actions. The analyst does not have access to the agent's information and ponders whether the observed actions could be justified through a rational Bayesian model with a known utility…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…