We consider the total variation minimization model with consistent finite element discretization. It has been shown in the literature that this model can be reformulated as a saddle-point problem and be efficiently solved by the primal-dual method. The convergence for this application of the primal-dual method has also been analyzed. In this paper, we focus … Read more
In this paper we address the Adjacent Quadratic Assignment Problem (AQAP) which is a variant of the QAP where the cost coefficient matrix has a particular structure. Motivated by strong lower bounds obtained by applying Reformulation Linearization Technique (RLT) to the classical QAP, we propose two special RLT representations for the problem. The first is … Read more
The Minimum Spanning Tree Problem (MSTP) is one of the most known combinatorial optimization problems. It concerns the determination of a minimum edge-cost subgraph spanning all the vertices of a given connected graph. The Quadratic Minimum Spanning Tree Problem (QMSTP) is a variant of the MST whose cost considers also the interaction between every pair … Read more
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