We address the minimization of the sum of a proper, convex and lower semicontinuous with a (possibly nonconvex) smooth function from the perspective of an implicit dynamical system of forward-backward type. The latter is formulated by means of the gradient of the smooth function and of the proximal point operator of the nonsmooth one. The … Read more
In recent years the expansion of energy supplies from volatile renewable sources has triggered an increased interest in stochastic optimization models for hydro-thermal unit commitment. Several studies have modelled this as a two-stage or multi-stage stochastic mixed-integer optimization problem. Solving such problems directly is computationally intractable for large instances, and alternative approaches are required. In … Read more
The recent expansion of renewable energy supplies has prompted the development of a variety of efficient stochastic optimization models and solution techniques for hydro-thermal scheduling. However, little has been published about the added value of stochastic models over deterministic ones. In the context of day-ahead and intraday unit commitment under wind uncertainty, we compare two-stage … Read more
We study the design of robust truss structures under mechanical equilibrium, displacements and stress constraints. Our main objective is to minimize the total amount of material, for the purpose of finding the most economic structure. A robust design is found by considering load perturbations. The nature of the constraints makes the mathematical program nonconvex. In … Read more
A direct-search derivative-free Matlab optimizer for bound-constrained problems is described, whose remarkable features are its ability to handle a mix of continuous and discrete variables, a versatile interface as well as a novel self-training option. Its performance compares favourably with that of NOMAD, a state-of-the art package. It is also applicable to multilevel equilibrium- or … Read more
The Johnson-Lindenstrauss lemma allows dimension reduction on real vectors with low distortion on their pairwise Euclidean distances. This result is often used in algorithms such as $k$-means or $k$ nearest neighbours since they only use Euclidean distances, and has sometimes been used in optimization algorithms involving the minimization of Euclidean distances. In this paper we … Read more
We propose a novel, Bayesian framework for assessing the relative strengths of data-driven ambiguity sets in distributionally robust optimization (DRO). The key idea is to measure the relative size between a candidate ambiguity set and an \emph{asymptotically optimal} set as the amount of data grows large. This asymptotically optimal set is provably the smallest convex … Read more
We discuss structured nonlinear programming problems arising in control applications, and we review software and hardware capabilities that enable the efficient exploitation of such structures. We focus on linear algebra parallelization strategies and discuss how these interact and influence high-level algorithmic design elements required to enforce global convergence and deal with negative curvature in a … Read more
We suppose the existence of an oracle which solves any semidefinite programming (SDP) problem satisfying Slater’s condition simultaneously at its primal and dual sides. We note that such an oracle might not be able to directly solve general SDPs even after certain regularization schemes are applied. In this work we fill this gap and show … Read more
Recently Chubanov proposed a method which solves homogeneous linear equality systems with positive variables in polynomial time. Chubanov’s method can be considered as a column-wise rescaling procedure. We adapt Chubanov’s method to the von Neumann problem, and so we design a polynomial time column-wise rescaling von Neumann algorithm. This algorithm is the first variant of … Read more