A widespread and successful approach to tackle unit-commitment problems is constraint decomposition: by dualizing the linking constraints, the large-scale nonconvex problem decomposes into smaller independent subproblems. The dual problem consists then in finding the best Lagrangian multiplier...

In this paper, we consider adjustable robust versions of convex optimization problems with uncertain constraints and objectives and show that under fairly general assumptions, a static robust solution provides a good approximation for these adjustable robust problems. An adjustable robust...

We show that the Hedge algorithm, a method that is widely used in Machine Learning, can be interpreted as a particular instance of Dual Averaging schemes, which have recently been introduced by Nesterov for regret minimization. Based on this interpretation, we establish three alternative methods...

This paper focuses on numerical evaluation techniques related to fluctuation theory for Lévy processes; they can be applied in various domains, e.g., in finance in the pricing of so-called barrier options. More specifically, with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\bar{X}_t:= \sup _{0\le s\le t} X_s$$</EquationSource> </InlineEquation> denoting the running...</equationsource></inlineequation>

We consider a generalization of the unsplittable maximum two-commodity flow problem on undirected graphs where each commodity <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${i \in \{1, 2\}}$$</EquationSource> </InlineEquation> can be split into a bounded number k <Subscript> i </Subscript> of equally-sized chunks that can be routed on different paths. We show that in contrast to the...</subscript></equationsource></inlineequation>

We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (Problemy Kibernet 10:119–139, <CitationRef CitationID="CR4">1963</CitationRef>) and Shapley (Naval Res Logist Q 14: 453–460, <CitationRef CitationID="CR11">1967</CitationRef>). First, we gain insight in this relation when we analyse...</citationref></citationref>

The main goal of this note is to give a counterexample to the Triality Theorem in Gao and Ruan (Math Methods Oper Res 67:479–491, <CitationRef CitationID="CR2">2008</CitationRef>). This is done first by considering a more general optimization problem with the aim to encompass several examples from Gao and Ruan (Math Methods Oper Res...</citationref>

We extend the theory of penalty functions to stochastic programming problems with nonlinear inequality constraints dependent on a random vector with known distribution. We show that the problems with penalty objective, penalty constraints and chance constraints are asymptotically equivalent...

Personal Rapid Transit (PRT) is a public transportation mode, in which small automated vehicles transport passengers on demand. Central control of the vehicles leads to interesting possibilities for optimized routings. The complexity of the involved routing problems together with the fact that...

The focus of this paper is on the asymptotics of large-time numbers of customers in time-periodic Markovian many-server queues with customer abandonment in heavy traffic. Limit theorems are obtained for the periodic number-of-customers processes under the fluid and diffusion scalings. Other...