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1	Locating a semi-obnoxious facility in the special case of Manhattan distances Wagner, Andrea January 2019 (has links) (PDF) The aim of thiswork is to locate a semi-obnoxious facility, i.e. tominimize the distances to a given set of customers in order to save transportation costs on the one hand and to avoid undesirable interactions with other facilities within the region by maximizing the distances to the corresponding facilities on the other hand. Hence, the goal is to satisfy economic and environmental issues simultaneously. Due to the contradicting character of these goals, we obtain a non-convex objective function. We assume that distances can be measured by rectilinear distances and exploit the structure of this norm to obtain a very efficient dual pair of algorithms.
2	Solving systems of monotone inclusions via primal-dual splitting techniques Bot, Radu Ioan, Csetnek, Ernö Robert, Nagy, Erika 20 March 2013 (has links) (PDF) In this paper we propose an algorithm for solving systems of coupled monotone inclusions in Hilbert spaces. The operators arising in each of the inclusions of the system are processed in each iteration separately, namely, the single-valued are evaluated explicitly (forward steps), while the set-valued ones via their resolvents (backward steps). In addition, most of the steps in the iterative scheme can be executed simultaneously, this making the method applicable to a variety of convex minimization problems. The numerical performances of the proposed splitting algorithm are emphasized through applications in average consensus on colored networks and image classification via support vector machines. convexe optimierung algorithmen convex minimization coupled systems forward-backward-forward algorithm monotone inclusion operator splitting 47H05 65K05 90C25 90C46 ddc:510 Algorithmus Operator-Splitting-Verfahren
3	Solving systems of monotone inclusions via primal-dual splitting techniques Bot, Radu Ioan, Csetnek, Ernö Robert, Nagy, Erika 20 March 2013 (has links) In this paper we propose an algorithm for solving systems of coupled monotone inclusions in Hilbert spaces. The operators arising in each of the inclusions of the system are processed in each iteration separately, namely, the single-valued are evaluated explicitly (forward steps), while the set-valued ones via their resolvents (backward steps). In addition, most of the steps in the iterative scheme can be executed simultaneously, this making the method applicable to a variety of convex minimization problems. The numerical performances of the proposed splitting algorithm are emphasized through applications in average consensus on colored networks and image classification via support vector machines. info:eu-repo/classification/ddc/510 ddc:510 convexe optimierung, algorithmen 47H05, 65K05, 90C25, 90C46

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