Related papers: Relaxation for an optimal design problem with line…
In many problems in optimal control, one seeks to minimise an objective function subject to constraints on the velocity of the system. Imposing these constraints directly -- the ``hard-constrained'' approach -- is often analytically and…
The problems of optimally estimating a phase, a direction, and the orientation of a Cartesian frame (or trihedron) with general pure states are addressed. Special emphasis is put on estimation schemes that allow for inconclusive answers or…
We give an overview over the usefulness of the concept of equivariance and invariance in the design of experiments for generalized linear models. In contrast to linear models here pairs of transformations have to be considered which act…
Resolvable designs with two blocks per replicate are studied from an optimality perspective. Because in practice the number of replicates is typically less than the number of treatments, arguments can be based on the dual of the information…
Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods struggle when adopted separately, their combination enabled by a…
A new, fully-localised, energy growth optimal is found over large times and in long pipe domains at a given mass flow rate. This optimal emerges at a threshold disturbance energy below which a nonlinear version of the known…
A design problem of finding an optimally stiff membrane structure by selecting one-dimensional fiber reinforcements is formulated and solved. The membrane model is derived in a novel manner from a particular three-dimensional linear elastic…
This paper proposes a method to compute lower performance bounds for discrete-time infinite-horizon min-max control problems with input constraints and bounded disturbances. Such bounds can be used as a performance metric for control…
The full-dimensional (metric, Euclidean, least squares) multidimensional scaling stress loss function is combined with a quadratic external penalty function term. The trajectory of minimizers of stress for increasing values of the penalty…
This paper proposes tight semidefinite relaxations for polynomial optimization. The optimality conditions are investigated. We show that generally Lagrange multipliers can be expressed as polynomial functions in decision variables over the…
In this paper, we consider the problem of optimal reinsurance design, when the risk is measured by a distortion risk measure and the premium is given by a distortion risk premium. First, we show how the optimal reinsurance design for the…
Minimizing the so-called "Dirichlet energy" with respect to the domain under a volume constraint is a standard problem in shape optimization which is now well understood. This article is devoted to a prototypal non-linear version of the…
We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…
In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of…
We consider the problem of inference in higher-order undirected graphical models with binary labels. We formulate this problem as a binary polynomial optimization problem and propose several linear programming relaxations for it. We compare…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
In this paper we address the speed planning problem for a vehicle along a predefined path. A weighted average of two (conflicting) terms, energy consumption and travel time, is minimized. After deriving a non-convex mathematical model of…
This work is concerned with a class of optimal control problems governed by a partial differential equation that are motivated by an application in radiotherapy treatment planning, where the primary design objective is to minimize the…
In power systems, large-scale optimisation problems are extensively used to plan for capacity expansion at the supra-national level. However, their cost-optimal solutions are often not exploitable by decision-makers who are preferably…
We perform a detailed study of a simple mathematical model addressing the problem of optimally regulating a process subject to periodic external forcing, which is interesting both in view of its direct applications and as a prototype for…