Chromatographic separation plays a vital role in various areas, as this technique can deliver high-quality products both in lab- and industrial-scale processes. Economical and also ecological benefits can be expected when optimizing such processes with mathematical methods. However, even small perturbations in the operating conditions can result in significantly altered results, which may lead to … Read more
In this paper, we show that minimax rational approximations can be enhanced by introducing a controlling parameter on the denominator of the rational function. This is implemented by adding a small set of linear constraints to the underlying optimization problem. The modification integrates naturally into approximation models formulated as linear programming problems. We demonstrate our … Read more
We consider an unconstrained multi-criteria optimization problem with finite sum objective functions. The proposed algorithm belongs to a non-monotone trust-region framework where additional sampling approach is used to govern the sample size and the acceptance of a candidate point. Depending on the problem, the method can result in a mini-batch or an increasing sample size … Read more
The Alternating Direction Method of Multipliers (ADMM) is widely recognized for its efficiency in solving separable optimization problems. However, its application to optimization on Riemannian manifolds remains a significant challenge. In this paper, we propose a novel inertial Riemannian gradient ADMM (iRG-ADMM) to solve Riemannian optimization problems with nonlinear constraints. Our key contributions are as … Read more
Mathematical modeling, simulation, and optimization can significantly support the development and characterization of chromatography steps in the biopharmaceutical industry. Particularly mechanistic models become preferably used, as these models, once carefully calibrated, can be employed for a reliable optimization. However, model calibration is a difficult task in this context due to high correlations between parameters, highly … Read more
Many discrete optimal control problems feature combinatorial constraints on the possible switching patterns, a common example being minimum dwell-time constraints. After discretizing to a finite time grid, for these and many similar types of constraints, it is possible to give a description of the convex hull of feasible (finite-dimensional) binary controls via extended formulations. In … Read more
The development of nonlinear optimization algorithms capable of performing reliably in the presence of noise has garnered considerable attention lately. This paper advocates for strategies to create noise-tolerant nonlinear optimization algorithms by adapting classical deterministic methods. These adaptations follow certain design guidelines described here, which make use of estimates of the noise level in the … Read more
The problem of minimizing the first eigenvalue of the Dirichlet Laplacian with respect to a union of m balls with fixed identical radii and variable centers in the plane is investigated in the present work. The existence of a minimizer is shown and the shape sensitivity analysis of the eigenvalue with respect to the centers’ … Read more
We consider dynamic gas transport optimization problems, which lead to large-scale and nonconvex mixed-integer nonlinear optimization problems (MINLPs) on graphs. Usually, the resulting instances are too challenging to be solved by state-of-the-art MINLP solvers. In this paper, we use graph decompositions to obtain multiple optimization problems on smaller blocks, which can be solved in parallel … Read more
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these estimators as the sample size goes to infinity, which is both of theoretical as well as practical interest. This area of … Read more