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In this paper, we describe a decomposition algorithm suitable for two-stage convex stochastic programs known as Generalized Benders Decomposition. For this algorithm we propose a new reformulation that incorporates a lower bound cut that serves as a warm-start, decreasing the overall computation time. Additionally, we test the performance of the proposed reformulation on two modifications of the algorithm (bunching and multicut) using numerical examples. The numerical part is programmed in MATLAB...
Let be a smooth oriented Riemannian manifold which is compact, connected, without boundary and with second homology group without torsion. In this paper we characterize the sequential
weak closure of smooth graphs in with equibounded Dirichlet energies, being the unit ball in . More precisely, weak limits of graphs of smooth maps with equibounded Dirichlet integral give rise to elements of the space (cf. [4], [5], [6]).
In this paper we prove that every element in is the weak limit...
Some criteria for weak compactness of set valued integrals are given. Also we show some applications to the study of multimeasures on Banach spaces with the Radon-Nikodym property.
In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the distributional Jacobian and the relaxed total variation, which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex functionals.
In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the distributional Jacobian and the relaxed total variation, which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex functionals.
We use tighter majorizing sequences than in earlier studies to provide a semilocal convergence analysis for the secant method. Our sufficient convergence conditions are also weaker. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.
Unilateral deflection problem of a clamped plate above a rigid inner obstacle is considered. The variable thickness of the plate is to be optimized to reach minimal weight under some constraints for maximal stresses. Since the constraints are expressed in terms of the bending moments only, Herrmann-Hellan finite element scheme is employed. The existence of an optimal thickness is proved and some convergence analysis for approximate penalized optimal design problem is presented.
Shape optimization of a two-dimensional elastic body is considered, provided the material is weakly supporting tension. The problem generalizes that of a masonry dam subjected to its own weight and to the hydrostatic presure. Existence of an optimal shape is proved. Using a penalty method and finite element technique, approximate solutions are proposed and their convergence is analyzed.
The problem to find an optimal thickness of the plate in a set of bounded Lipschitz continuous functions is considered. Mean values of the intensity of shear stresses must not exceed a given value. Using a penalty method and finite element spaces with interpolation to overcome the “locking” effect, an approximate optimization problem is proposed. We prove its solvability and present some convergence analysis.
We investigate a global-in-time variational approach to abstract evolution
by means of the weighted energy-dissipation functionals proposed by Mielke and Ortiz [ESAIM: COCV14 (2008) 494–516]. In particular, we focus on
gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow.
Sharp convergence rates are provided and the convergence analysis is combined with time-discretization....
We investigate a global-in-time variational approach to abstract evolution
by means of the weighted energy-dissipation functionals proposed by Mielke and Ortiz [ESAIM: COCV14 (2008) 494–516]. In particular, we focus on
gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow.
Sharp convergence rates are provided and the convergence analysis is combined with time-discretization....
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