Related papers: Robust optimization with belief functions
Uncertain partially observable Markov decision processes (uPOMDPs) allow the probabilistic transition and observation functions of standard POMDPs to belong to a so-called uncertainty set. Such uncertainty, referred to as epistemic…
Budgeted uncertainty sets have been established as a major influence on uncertainty modeling for robust optimization problems. A drawback of such sets is that the budget constraint only restricts the global amount of cost increase that can…
A classical portfolio theory deals with finding the optimal proportion in which an agent invests a wealth in a risk-free asset and a probabilistic risky asset. Formulating and solving the problem depend on how the risk is represented and…
We consider solving linear optimization (LO) problems with uncertain objective coefficients. For such problems, we often employ robust optimization (RO) approaches by introducing an uncertainty set for the unknown coefficients. Typical RO…
Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems,…
We study an optimization-based approach to construct statistically accurate confidence intervals for simulation performance measures under nonparametric input uncertainty. This approach computes confidence bounds from simulation runs driven…
In a real expert system, one may have unreliable, unconfident, conflicting estimates of the value for a particular parameter. It is important for decision making that the information present in this aggregate somehow find its way into use.…
It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…
Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…
We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal…
We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In…
Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…
We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables. The probability distributions for these random parameters are…
We tackle robust optimization problems under objective uncertainty in the oracle model, i.e., when the deterministic problem is solved by an oracle. The oracle-based setup is favorable in many situations, e.g., when a compact formulation of…
Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first…
We consider the problem of minimizing a convex function that depends on an uncertain parameter $\theta$. The uncertainty in the objective function means that the optimum, $x^*(\theta)$, is also a function of $\theta$. We propose an…
Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We analyze this approach for a class of selection problems. The aim is to choose…
Many optimization problems incorporate uncertainty affecting their parameters and thus their objective functions and constraints. As an example, in chance-constrained optimization the constraints need to be satisfied with a certain…
In this paper, we introduce a deterministic formulation for the geometric programming problem, wherein the coefficients are represented as independent linear-normal uncertain random variables. To address the challenges posed by this…
The main aim of decision support systems is to find solutions that satisfy user requirements. Often, this leads to predictability of those solutions, in the sense that having the input data and the model, an adversary or enemy can predict…