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We consider a generic class of chance-constrained optimization problems with heavy-tailed (i.e., power-law type) risk factors. In this setting, we use the scenario approach to obtain a constant approximation to the optimal solution with a…
Stochastic shortest path computations are often performed under very strict time constraints, so computational efficiency is critical. A major determinant for the CPU time is the number of scenarios used. We demonstrate that by carefully…
The optimization of power systems involves complex uncertainties, such as technological progress, political context, geopolitical constraints. Negotiations at COP21 are complicated by the huge number of scenarios that various people want to…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
This paper proposes a reformulation of the scenario-based two-stage unit commitment problem under uncertainty that allows finding unit-commitment plans that perform reasonably well both in expectation and for the worst case realization of…
We investigate the connections between compression learning and scenario based optimization. We first show how to strengthen, or relax the consistency assumption at the basis of compression learning and study the learning and generalization…
Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe…
Scenario reduction (SR) aims to identify a small yet representative scenario set to depict the underlying uncertainty, which is critical to scenario-based stochastic optimization (SBSO) of power systems. Existing SR techniques commonly aim…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
A decision rule is epsilon-minimax if it is minimax up to an additive factor epsilon. We present an algorithm for provably obtaining epsilon-minimax solutions for a class of statistical decision problems. In particular, we are interested in…
We give a method for proactively identifying small, plausible shifts in distribution which lead to large differences in model performance. These shifts are defined via parametric changes in the causal mechanisms of observed variables, where…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
Security-constrained unit commitment (SCUC) model is used for power system day-ahead scheduling. However, current SCUC model uses a static network to deliver power and meet demand optimally. A dynamic network can provide a lower optimal…
A fundamental model of quantum computation is the programmable quantum gate array. This is a quantum processor that is fed by a program state that induces a corresponding quantum operation on input states. While being programmable, any…
This paper studies chance-constrained stochastic optimization problems with finite support. It presents an iterative method that solves reduced-size chance-constrained models obtained by partitioning the scenario set. Each reduced problem…
Modeling decision-dependent scenario probabilities in stochastic programs is difficult and typically leads to large and highly non-linear MINLPs that are very difficult to solve. In this paper, we develop a new approach to obtain a compact…
We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…
Procrustes problems are matrix approximation problems searching for a~transformation of the given dataset to fit another dataset. They find applications in numerous areas, such as factor and multivariate analysis, computer vision,…