We investigate here the robust stabilization problem for the descriptor discrete time systems and build an optimal solution in the case when both the nominal system and the perturbations are given in terms of left coprime factorizations. Moreover our formulas are given straight from the original data, using solely the stabilizing solutions of two Riccati … Read more
Private investors, flexibility, efficiency and environmental requirements from deregulated markets have led the existence and building of a significant number of combined-cycle gas turbines (CCGTs) in many power systems. These plants represent a complicated optimization problem for the short-term planning unit commitment (UC) carried out by independent system operators due to their multiple operating configurations. … Read more
Covering problems are well studied in the Operations Research literature under the assumption that both the set of users and the set of potential facilities are finite. In this paper we address the following variant, which leads to a Mixed Integer Nonlinear Program (MINLP): locations of p facilities are sought along the edges of a … Read more
It is shown that a recently proposed method by Chubanov for solving linear homogeneous systems with positive variables can be improved, both theoretically and computationally. Citation TU Delft, September 2014 Article Download View Speeding up Chubanov's Basic Procedure
We present a filter line-search algorithm that does not require inertia information about the linear system to ensure global convergence. The proposed approach performs curvature tests along the search step to ensure descent. This feature permits more modularity in the linear algebra, enabling the use of a wider range of iterative and decomposition strategies. We … Read more
Abstract— The increasing penetration of uncertain generation such as wind and solar in power systems imposes new challenges to the Unit Commitment (UC) problem, one of the most critical tasks in power systems operations. The two most common approaches to address these challenges — stochastic and robust optimization — have drawbacks that prevent or restrict their … Read more
Multistage stochastic mixed-integer programming is a powerful modeling paradigm appropriate for many problems involving a sequence of discrete decisions under uncertainty; however, they are difficult to solve without exploiting special structures. We present scenario-tree decomposition to establish bounds for unstructured multistage stochastic mixed-integer programs. Our method decomposes the scenario tree into a number of smaller … Read more
The main contributions of this thesis are the comparison of existing and the design of new exact approaches based on linear, quadratic and semidefinite relaxations for row layout problems and several applications in logistic. In particular we demonstrate that our suggested semidefinite approach is the strongest exact method to date for most row layout problems. … Read more
Ordering problems are a special class of combinatorial optimization problems, where weights are assigned to each ordering of n objects and the aim is to find an ordering of maximum weight. Even for the simplest case of a linear cost function, ordering problems are known to be NP-hard, i.e. it is extremely unlikely that there … Read more
We consider the linearly constrained convex minimization model with a separable objective function which is the sum of m functions without coupled variables, and discuss how to design an efficient algorithm based on the fundamental technique of splitting the augmented Lagrangian method (ALM). Our focus is the specific big-data scenario where m is huge. A … Read more