We study the problem of finding the Lowner-John ellipsoid, i.e., an ellipsoid with minimum volume that contains a given convex set. We reformulate the problem as a generalized copositive program, and use that reformulation to derive tractable semidefinite programming approximations for instances where the set is defined by affine and quadratic inequalities. We prove that, … Read more
The global container shipping network is vital to international trade. Current techniques for its vulnerability assessment are constrained due to the lack of historical disruption data and computational limitations due to typical network sizes. We address these modelling challenges by developing a new framework, composed by game-theoretic attacker-defender model and a cost-based container assignment model … Read more
We propose a convex-optimization-based framework for computation of invariant measures of polynomial dynamical systems and Markov processes, in discrete and con- tinuous time. The set of all invariant measures is characterized as the feasible set of an infinite-dimensional linear program (LP). The objective functional of this LP is then used to single-out a specific measure … Read more
We consider the problem of approximating numerically the moments and the supports of measures which are invariant with respect to the dynamics of continuousand discrete-time polynomial systems, under semialgebraic set constraints. First, we address the problem of approximating the density and hence the support of an invariant measure which is absolutely continuous with respect to … Read more
We study the weighted induced bipartite subgraph problem (WIBSP). The goal of WIBSP is, given a graph and nonnegative weights for the nodes, to find a set W of nodes with the maximum total weight such that a subgraph induced by W is bipartite. WIBSP is also referred as to the graph bipartization problem or … Read more
In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the sparsity of the involved matrices and solves the problem via solving a sequence of positive definite system of linear equations after identifying … Read more
In the daily operations of ThyssenKrupp Presta AG, ball nut assemblies (BNA) undergo a vibroacoustical quality test and are binary classified based on their order spectra. In this work we formulate a multiple change point problem and derive optimal quality intervals and thresholds for the order spectra that minimize the number of incorrectly classified BNA. … Read more
Within this work, we present a warm-started algorithm for Model Predictive Control (MPC) of switched nonlinear systems under combinatorial constraints based on Combinatorial Integral Approximation (CIA). To facilitate high-speed solutions, we introduce a preprocessing step for complexity reduction of CIA problems, and include this approach within a new toolbox for solution of CIA problems with … Read more
This paper aims to advance decision-making in power systems by proposing an integrated framework that combines sensor data analytics and optimization. Our modeling framework consists of two components: (1) a predictive analytics methodology that uses real-time sensor data to predict future degradation and remaining lifetime of generators as a function of the loading conditions, and … Read more
Empty freight car allocation problems as well as eet sizing problems depict highly important topics in the eld of railway cargo optimization. Fleet sizing is mainly used in order to nd the minimal number of freight cars ( xed costs) needed to operate the transportation network successfully (e.g. satisfy customer demands). After a consignment is transported … Read more