A class of interior point methods using inexact directions is analysed. The linear system arising in interior point methods for linear programming is reformulated such that the solution is less sensitive to perturbations in the right-hand side. For the new system an implementable condition is formulated that controls the relative error in the solution. Based … Read more
Recently increasing penetration of renewable energy generation brings challenges for power system operators to perform efficient power generation daily scheduling, due to the intermittent nature of the renewable generation and discrete decisions of each generation unit. Among all aspects to be considered, unit commitment polytope is fundamental and embedded in the models at different stages … Read more
Variants of the coordinate descent approach for minimizing a nonlinear function are distinguished in part by the order in which coordinates are considered for relaxation. Three common orderings are cyclic (CCD), in which we cycle through the components of $x$ in order; randomized (RCD), in which the component to update is selected randomly and independently … Read more
In this paper, we describe a two-stage method for solving optimization problems with bound constraints. It combines the active-set estimate described in [Facchinei and Lucidi, 1995] with a modification of the non-monotone line search framework recently proposed in [De Santis et al., 2012]. In the first stage, the algorithm exploits a property of the active-set … Read more
A path-block cycle is a graph that consists of several cycles that all intersect in a common subset of nodes. The associated path-block-cycle inequalities are valid, and sometimes facet-defining, inequalities for polytopes in connection with graph partitioning problems and corresponding multicut problems. Special cases of the inequalities were introduced by De Souza & Laurent (1995) … Read more
This paper proposes a method for eliminating multicollinearity from linear regression models. Specifically, we select the best subset of explanatory variables subject to the upper bound on the condition number of the correlation matrix of selected variables. We first develop a cutting plane algorithm that, to approximate the condition number constraint, iteratively appends valid inequalities … Read more
In this paper, we consider how to directly apply the BFGS method to finding a zero point of any given monotone gradient and thus suggest new conditions to locate the corresponding step lengths. The suggested conditions involve curvature condition and merely use gradients’ computations. Furthermore, they can guarantee convergence without any other restrictions. Finally, preliminary … Read more
We study conditions under which the objective functions of a multi-objective 0-1 integer linear program guarantee the existence of an ideal point, meaning the existence of a feasible solution that simultaneously minimizes all objectives. In addition, we study the complexity of recognizing whether a set of objective functions satisfies these conditions: we show that it … Read more
We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of pieces can be exponentially large. A significant challenge in designing a practical piecewise affine policy is constructing good pieces of … Read more
Standard load profiles (SLPs) are used to calculate the natural gas demand of non-daily metered customers based on temperature forecasts. The most recent version of natural gas SLPs in Germany was published by the Federal Association of Energy and Water in June 2015. With the concept SigLinDE, a linearization of the old SLPs was carried … Read more