Although modern societies strive towards energy systems that are entirely based on renewable energy carriers, natural gas is still one of the most important energy sources. This became even more obvious in Europe with Russia’s 2022 war against the Ukraine and the resulting stop of gas supplies from Russia. Besides that it is very important … Read more
The growing proliferation of wind power into the power grid achieves a low-cost sustainable electricity supply while introducing technical challenges with associated intermittency. This paper proposes a fully adaptive distributionally robust multistage framework based on mixed decision rules (MDR) for generation scheduling under uncertainty to adapt wind power respecting non-anticipativity in quick-start unit status decision … Read more
We propose a novel steplength selection rule in proximal gradient methods for minimizing the sum of a differentiable function plus an ℓ1-norm penalty term. The proposed rule modifies one of the classical Barzilai-Borwein steplength, extending analogous results obtained in the context of gradient projection methods for constrained optimization. We analyze the spectral properties of the … Read more
In large scale applications, deterministic and stochastic variants of Cauchy’s steepest descent method are widely used for the minimization of objectives that are only piecewise smooth. In this paper we analyse a deterministic descent method based on the generalization of rescaled conjugate gradients proposed by Philip Wolfe in 1975 for objectives that are convex. Without … Read more
In this paper, we look into the rotated quadratic cone and analyze its algebraic structure. We construct an algebra associated with this cone and show that this algebra is a Euclidean Jordan algebra (EJA) with a certain inner product. We also demonstrate some spectral and algebraic characteristics of this EJA. The rotated quadratic cone is … Read more
In the min-Knapsack problem, one is given a set of items, each having a certain cost and weight. The objective is to select a subset with minimum cost, such that the sum of the weights is not smaller than a given constant. In this paper we introduce an extension of the min-Knapsack problem with additional … Read more
We consider optimization problems with objective and constraint being the difference of convex and weakly convex functions. This framework covers a vast family of nonsmooth and nonconvex optimization problems, particularly those involving Difference-of-Convex (DC) functions with known DC decomposition, functions whose gradient is Lipschitz continuous, as well as problems that comprise certain classes of composite … Read more
\(\) In this paper we consider finding an approximate second-order stationary point (SOSP) of general nonconvex conic optimization that minimizes a twice differentiable function subject to nonlinear equality constraints and also a convex conic constraint. In particular, we propose a Newton-conjugate gradient (Newton-CG) based barrier-augmented Lagrangian method for finding an approximate SOSP of this problem. … Read more
Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modeled as the solution to an optimization problem. Here the exact gradient with respect to the hyperparameters cannot be feasibly computed and approximate strategies are required. We introduce a unified framework for computing hypergradients that … Read more
In this work, we design primal and dual bounding methods for multistage adjustable robust optimization (MSARO) problems by adapting two decision rules rooted in the stochastic programming literature. This approach approximates the primal and dual formulations of an MSARO problem with two-stage models. From the primal perspective, this is achieved by applying two-stage decision rules … Read more