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High-dimensional complex multi-parameter problems are prevalent in engineering, exceeding the capabilities of traditional surrogate models designed for low/medium-dimensional problems. These models face the curse of dimensionality,…
In this paper a class of combinatorial optimization problems is discussed. It is assumed that a solution can be constructed in two stages. The current first-stage costs are precisely known, while the future second-stage costs are only known…
Multistage robust optimization problems can be interpreted as two-person zero-sum games between two players. We exploit this game-like nature and utilize a game tree search in order to solve quantified integer programs (QIPs). In this…
An algorithm is proposed to solve robust control problems constrained by partial differential equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels in this MG/OPT hierarchy correspond to discretization…
We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…
We investigate the adaptive robust control framework for portfolio optimization and loss-based hedging under drift and volatility uncertainty. Adaptive robust problems offer many advantages but require handling a double optimization problem…
Decision support systems often rely on solving complex optimization problems that may require to estimate uncertain parameters beforehand. Recent studies have shown how using traditionally trained estimators for this task can lead to…
Optimization models used to make discrete decisions often contain uncertain parameters that are context-dependent and estimated through prediction. To account for the quality of the decision made based on the prediction, decision-focused…
Safe navigation in real-time is challenging because engineers need to work with uncertain vehicle dynamics, variable external disturbances, and imperfect controllers. A common safety strategy is to inflate obstacles by hand-defined margins.…
This paper presents a methodological framework for training, self-optimising, and self-organising surrogate models to approximate and speed up multiobjective optimisation of technical systems based on multiphysics simulations. At the hand…
In this paper we present an algorithm for yield estimation and optimization exploiting Hessian based optimization methods, an adaptive Monte Carlo (MC) strategy, polynomial surrogates and several error indicators. Yield estimation is used…
In the present work, we consider multi-fidelity surrogate modelling to fuse the output of multiple aero-servo-elastic computer simulators of varying complexity. In many instances, predictions from multiple simulators for the same quantity…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many financial models such prices can be approximated by means of…
Portfolio selection in the periodic investment of securities modeled by a multivariate Merton model with dependent jumps is considered. The optimization framework is designed to maximize expected terminal wealth when portfolio risk is…
A challenging problem in both engineering and computer science is that of minimising a function for which we have no mathematical formulation available, that is expensive to evaluate, and that contains continuous and integer variables, for…
Many real-world decisions are made under uncertainty by solving optimization problems using predicted quantities. This predict-then-optimize paradigm has motivated decision-focused learning, which trains models with awareness of how the…
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…
We consider the numerical approximation of $\mathbb{P}[G\in \Omega]$ where the $d$-dimensional random variable $G$ cannot be sampled directly, but there is a hierarchy of increasingly accurate approximations $\{G_\ell\}_{\ell\in\mathbb{N}}$…
Simulation models are widely used in practice to facilitate decision-making in a complex, dynamic and stochastic environment. But they are computationally expensive to execute and optimize, due to lack of analytical tractability. Simulation…