Related papers: Combinatorial two-stage minmax regret problems und…
In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at…
Least worst regret (and sometimes minimax) analysis are often used for decision making whenever it is difficult, or inappropriate, to attach probabilities to possible future scenarios. We show that, for each of these two approaches and…
We consider algorithms for "smoothed online convex optimization" problems, a variant of the class of online convex optimization problems that is strongly related to metrical task systems. Prior literature on these problems has focused on…
The parallel machine scheduling problem has been a popular topic for many years due to its theoretical and practical importance. This paper addresses the robust makespan optimization problem on unrelated parallel machine scheduling with…
Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered. Usually, a robust problem becomes harder to…
The parameters for a Markov Decision Process (MDP) often cannot be specified exactly. Uncertain MDPs (UMDPs) capture this model ambiguity by defining sets which the parameters belong to. Minimax regret has been proposed as an objective for…
This paper deals with a robust recoverable approach to 0-1 programming problems. It is assumed that a solution constructed in the first stage can be modified to some extent in the second stage. This modification consists in choosing a…
Multi-objective optimization studies the process of seeking multiple competing desiderata in some operation. Solution techniques highlight marginal tradeoffs associated with weighing one objective over others. In this paper, we consider…
In this paper the minimum spanning tree problem with uncertain edge costs is discussed. In order to model the uncertainty a discrete scenario set is specified and a robust framework is adopted to choose a solution. The min-max, min-max…
In this paper the following selection problem is discussed. A set of $n$ items is given and we wish to choose a subset of exactly $p$ items of the minimum total cost. This problem is a special case of 0-1 knapsack in which all the item…
We study two-stage robust optimization problems with mixed discrete-continuous decisions in both stages. Despite their broad range of applications, these problems pose two fundamental challenges: (i) they constitute infinite-dimensional…
Mechanism design has found considerable application to the construction of agent-interaction protocols. In the standard setting, the type (e.g., utility function) of an agent is not known by other agents, nor is it known by the mechanism…
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 this paper we study the mincut problem in the online setting. We consider two distinct models: A) competitive analysis and B) regret analysis. In the competitive setting we consider the vertex arrival model; whenever a new vertex arrives…
In this work, we consider two-stage quadratic optimization problems under ellipsoidal uncertainty. In the first stage, one needs to decide upon the values of a subset of optimization variables (control variables). In the second stage, the…
We introduce an online convex optimization algorithm which utilizes projected subgradient descent with optimal adaptive learning rates. Our method provides second-order minimax-optimal dynamic regret guarantee (i.e. dependent on the sum of…
Robust optimization typically follows a worst-case perspective, where a single scenario may determine the objective value of a given solution. Accordingly, it is a challenging task to reduce the size of an uncertainty set without changing…
In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the…
In decision-making under uncertainty, several criteria have been studied to aggregate the performance of a solution over multiple possible scenarios. This paper introduces a novel variant of ordered weighted averaging (OWA) for optimization…
This paper studies binary linear programming problems in the presence of uncertainties that may cause solution values to change during implementation. This type of uncertainty, termed implementation uncertainty, is modeled explicitly…