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1	On the Efficient Solution of Variational Inequalities; Complexity and Computational Efficiency Perakis, Georgia, Zaretsky, M. (Marina) 01 1900 (has links) In this paper we combine ideas from cutting plane and interior point methods in order to solve variational inequality problems efficiently. In particular, we introduce a general framework that incorporates nonlinear as well as linear "smarter" cuts. These cuts utilize second order information on the problem through the use of a gap function. We establish convergence as well as complexity results for this framework. Moreover, in order to devise more practical methods, we consider an affine scaling method as it applies to symmetric, monotone variationalinequality problems and demonstrate its convergence. Finally, in order to further improve the computational efficiency of the methods in this paper, we combine the cutting plane approach with the affine scaling approach.
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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