This paper is devoted to the study of unconstrained planar multiobjective location problems, where distances between points are defined by means of the Manhattan norm. By identifying all nonessential objectives, we develop an effective algorithm for generating the whole set of efficient solutions. We prove the correctness of this algorithm and present some computational results, … Read more
Low-rank tensor methods provide efficient representations and computations for high-dimensional problems and are able to break the curse of dimensionality when dealing with systems involving multiple parameters. We present algorithms for constrained nonlinear optimization problems that use low-rank tensors and apply them to optimal control of PDEs with uncertain parameters and to parametrized variational inequalities. … Read more
Investment decisions in renewable energy sources such as small hydro, wind power, biomass and solar are frequently made in the context of enormous uncertainty surrounding both intermittent generation and the highly volatile electricity spot prices that are used for clearing of trades. This paper presents a new portfolio-based approach for selecting long-term investments in small-scale … Read more
The general ellipse packing problem is to find a non-overlapping arrangement of 𝑛 ellipses with (in principle) arbitrary size and orientation parameters inside a given type of container set. Here we consider the general ellipse packing problem with respect to an optimized circle container with minimal radius. Following the review of selected topical literature, we … Read more
We present three new approximate versions of alternating direction method of multipliers (ADMM), all of which require only knowledge of subgradients of the subproblem objectives, rather than bounds on the distance to the exact subproblem solution. One version, which applies only to certain common special cases, is based on combining the operator-splitting analysis of the … Read more
In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable by a polynomial or a rational function, then the semi-infinite program can be reformulated as an equivalent semidefinite program. Solving this … Read more
In radiation therapy planning, uncertainties in target volume definition yield a risk of underdosing the tumor. The classical way to prevent this in the context of external beam radiotherapy (EBRT) has been to expand the clinical target volume (CTV) with an isotropic margin to obtain the planning target volume (PTV). However, the EBRT-based PTV concept … Read more
We consider the decision problem of making causal conclusions from observational data. Typically, using standard matched pairs techniques, there is a source of uncertainty that is not usually quanti fied, namely the uncertainty due to the choice of the experimenter: two di fferent reasonable experimenters can easily have opposite results. In this work we present an alternative … Read more
Pathfinding problems consist in determining the optimal shortest path, or at least one path, between two points in the space. In this paper, we propose a particular approach, based on methods used in Computational Fluid Dynamics, that intends to solve such problems. In particular, we reformulate pathfinding problems as the motion of a viscous fluid … Read more
The development of mathematical simulation and optimization models and algorithms for solving gas transport problems is an active field of research. In order to test and compare these models and algorithms, gas network instances together with demand data are needed. The goal of GasLib is to provide a set of publicly available gas network instances … Read more