The Experts below are selected from a list of 23178 Experts worldwide ranked by ideXlab platform
Manfred Morari - One of the best experts on this subject based on the ideXlab platform.
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a decomposition method for large scale milps with performance guarantees and a power system application
Automatica, 2016Co-Authors: Robin Vujanic, Peyman Mohajerin Esfahani, Paul J Goulart, Sebastien Mariethoz, Manfred MorariAbstract:Lagrangian duality in mixed integer optimization is a useful framework for Problem decomposition and for producing tight lower bounds to the optimal objective. However, in contrast to the convex case, it is generally unable to produce optimal solutions directly. In fact, solutions recovered from the dual may not only be suboptimal, but even infeasible. In this paper we concentrate on large scale mixed-integer programs with a specific structure that appears in a variety of application domains such as power systems and supply chain management. We propose a solution method for these structures, in which the Primal Problem is modified in a certain way, guaranteeing that the solutions produced by the corresponding dual are feasible for the original unmodified Primal Problem. The modification is simple to implement and the method is amenable to distributed computation. We also demonstrate that the quality of the solutions recovered using our procedure improves as the Problem size increases, making it particularly useful for large scale Problem instances for which commercial solvers are inadequate. We illustrate the efficacy of our method with extensive experimentations on a Problem stemming from power systems.
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a decomposition method for large scale milps with performance guarantees and a power system application
arXiv: Optimization and Control, 2014Co-Authors: Robin Vujanic, Peyman Mohajerin Esfahani, Paul J Goulart, Sebastien Mariethoz, Manfred MorariAbstract:Lagrangian duality in mixed integer optimization is a useful framework for Problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce optimal solutions directly. In fact, solutions recovered from the dual may be not only suboptimal, but even infeasible. In this paper we concentrate on large scale mixed--integer programs with a specific structure that is of practical interest, as it appears in a variety of application domains such as power systems or supply chain management. We propose a solution method for these structures, in which the Primal Problem is modified in a certain way, guaranteeing that the solutions produced by the corresponding dual are feasible for the original unmodified Primal Problem. The modification is simple to implement and the method is amenable to distributed computations. We also demonstrate that the quality of the solutions recovered using our procedure improves as the Problem size increases, making it particularly useful for large scale instances for which commercial solvers are inadequate. We illustrate the efficacy of our method with extensive experimentations on a Problem stemming from power systems.
Patrick Jaap - One of the best experts on this subject based on the ideXlab platform.
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solving Primal plasticity increment Problems in the time of a single predictor corrector iteration
Computational Mechanics, 2020Co-Authors: Oliver Sander, Patrick JaapAbstract:The Truncated Nonsmooth Newton Multigrid (TNNMG) method is a well-established method for the solution of strictly convex block-separably nondifferentiable minimization Problems. It achieves multigrid-like performance even for non-smooth nonlinear Problems, while at the same time being globally convergent and without employing penalty parameters. We show that the algorithm can be applied to the Primal Problem of classical small-strain elastoplasticity with hardening. Numerical experiments show that the method is considerably faster than classical predictor–corrector methods. Indeed, solving an entire increment Problem with TNNMG can take less time than a single predictor–corrector iteration for the same Problem. At the same time, memory consumption is reduced considerably, in particular for three-dimensional Problems. Since the algorithm does not rely on differentiability of the objective functional, nonsmooth yield laws can be easily incorporated. The method is closely related to a predictor–corrector scheme with a consistent tangent predictor and line search. We explain the algorithm, prove global convergence, and show its efficiency using standard benchmarks from the literature.
Oliver Sander - One of the best experts on this subject based on the ideXlab platform.
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solving Primal plasticity increment Problems in the time of a single predictor corrector iteration
Computational Mechanics, 2020Co-Authors: Oliver Sander, Patrick JaapAbstract:The Truncated Nonsmooth Newton Multigrid (TNNMG) method is a well-established method for the solution of strictly convex block-separably nondifferentiable minimization Problems. It achieves multigrid-like performance even for non-smooth nonlinear Problems, while at the same time being globally convergent and without employing penalty parameters. We show that the algorithm can be applied to the Primal Problem of classical small-strain elastoplasticity with hardening. Numerical experiments show that the method is considerably faster than classical predictor–corrector methods. Indeed, solving an entire increment Problem with TNNMG can take less time than a single predictor–corrector iteration for the same Problem. At the same time, memory consumption is reduced considerably, in particular for three-dimensional Problems. Since the algorithm does not rely on differentiability of the objective functional, nonsmooth yield laws can be easily incorporated. The method is closely related to a predictor–corrector scheme with a consistent tangent predictor and line search. We explain the algorithm, prove global convergence, and show its efficiency using standard benchmarks from the literature.
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solving Primal plasticity increment Problems in the time of a single predictor corrector iteration
arXiv: Numerical Analysis, 2017Co-Authors: Oliver SanderAbstract:The Truncated Nonsmooth Newton Multigrid (TNNMG) method is a well-established method for the solution of strictly convex block-separably nondifferentiable minimization Problems. It achieves multigrid-like performance even for non-smooth nonlinear Problems, while at the same time being globally convergent and without employing penalty parameters. We show that the algorithm can be applied to the Primal Problem of classical linear elastoplasticity with hardening. Numerical experiments show that the method is considerably faster than classical predictor-corrector methods. Indeed, solving an entire increment Problem with TNNMG takes less time than a single predictor-corrector iteration for the same Problem. Since the algorithm does not rely on differentiability of the objective functional, nonsmooth yield functions like the Tresca yield function can be easily incorporated. The method is closely related to a predictor-corrector scheme with a consistent tangent predictor and line search. We explain the algorithm, prove global convergence, and show its efficiency using a standard benchmark from the literature.
Olivier Chapelle - One of the best experts on this subject based on the ideXlab platform.
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Training a support vector machine in the Primal
Neural Comput, 2007Co-Authors: Olivier ChapelleAbstract:Most literature on support vector machines (SVMs) concentrates on the dual optimization Problem. In this letter, we point out that the Primal Problem can also be solved efficiently for both linear and nonlinear SVMs and that there is no reason for ignoring this possibility. On the contrary, from the Primal point of view, new families of algorithms for large-scale SVM training can be investigated.
Martin Kruczenski - One of the best experts on this subject based on the ideXlab platform.
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s matrix bootstrap in 3 1 dimensions regularization and dual convex Problem
Journal of High Energy Physics, 2021Co-Authors: Martin KruczenskiAbstract:The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing, unitarity, and other constraints. For the 2 → 2 scattering matrix S2→2 such space is an infinite dimensional convex space whose boundary can be determined by maximizing linear functionals. On the boundary interesting theories can be found, many times at vertices of the space. Here we consider 3 + 1 dimensional theories and focus on the equivalent dual convex minimization Problem that provides strict upper bounds for the regularized Primal Problem and has interesting practical and physical advantages over the Primal Problem. Its variables are dual partial waves kl(s) that are free variables, namely they do not have to obey any crossing, unitarity or other constraints. Nevertheless they are directly related to the partial waves fl(s), for which all crossing, unitarity and symmetry properties result from the minimization. Numerically, it requires only a few dual partial waves, much as one wants to possibly match experimental results. We consider the case of scalar fields which is related to pion physics.
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S-matrix bootstrap in 3+1 dimensions: regularization and dual convex Problem
2021Co-Authors: Martin KruczenskiAbstract:The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing, unitarity, and other constraints. For the $2\rightarrow 2$ scattering matrix $S_{2\rightarrow 2}$ such space is an infinite dimensional convex space whose boundary can be determined by maximizing linear functionals. On the boundary interesting theories can be found, many times at vertices of the space. Here we consider $3+1$ dimensional theories and focus on the equivalent dual convex minimization Problem that provides strict upper bounds for the regularized Primal Problem and has interesting practical and physical advantages over the Primal Problem. Its variables are dual partial waves $k_\ell(s)$ that are free variables, namely they do not have to obey any crossing, unitarity or other constraints. Nevertheless they are directly related to the partial waves $f_\ell(s)$, for which all crossing, unitarity and symmetry properties result from the minimization. Numerically, it requires only a few dual partial waves, much as one wants to possibly match experimental results. We consider the case of scalar fields which is related to pion physics.
