The Experts below are selected from a list of 3534 Experts worldwide ranked by ideXlab platform
Michael M Zavlanos - One of the best experts on this subject based on the ideXlab platform.
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complexity certification of a distributed augmented lagrangian method
IEEE Transactions on Automatic Control, 2018Co-Authors: Soomin Lee, Nikolaos Chatzipanagiotis, Michael M ZavlanosAbstract:In this paper, we present complexity certification results for a distributed augmented Lagrangian (AL) algorithm used to solve convex optimization problems involving globally coupled linear constraints. Our method relies on the accelerated distributed AL (ADAL) algorithm, which can handle the coupled linear constraints in a distributed manner based on local estimates of the AL. We show that the theoretical complexity of ADAL to reach an $\epsilon$ -optimal solution both in terms of suboptimality and infeasibility is $O(\frac{1}{\epsilon })$ iterations. Moreover, we provide a valid upper bound for the optimal Dual Multiplier, which enables us to explicitly specify these complexity bounds. We also show how to choose the step-size parameter to minimize the bounds on the convergence rates. Finally, we discuss a motivating example, a model predictive control problem, involving a finite number of subsystems, which interact with each other via a general network.
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complexity certification of a distributed augmented lagrangian method
arXiv: Optimization and Control, 2017Co-Authors: Soomin Lee, Nikolaos Chatzipanagiotis, Michael M ZavlanosAbstract:In this paper we present complexity certification results for a distributed Augmented Lagrangian (AL) algorithm used to solve convex optimization problems involving globally coupled linear constraints. Our method relies on the Accelerated Distributed Augmented Lagrangian (ADAL) algorithm, which can handle the coupled linear constraints in a distributed manner based on local estimates of the AL. We show that the theoretical complexity of ADAL to reach an $\epsilon$-optimal solution both in terms of suboptimality and infeasibility is $O(\frac{1}{\epsilon})$ iterations. Moreover, we provide a valid upper bound for the optimal Dual Multiplier which enables us to explicitly specify these complexity bounds. We also show how to choose the stepsize parameter to minimize the bounds on the convergence rates. Finally, we discuss a motivating example, a model predictive control (MPC) problem, involving a finite number of subsystems which interact with each other via a general network.
Soomin Lee - One of the best experts on this subject based on the ideXlab platform.
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complexity certification of a distributed augmented lagrangian method
IEEE Transactions on Automatic Control, 2018Co-Authors: Soomin Lee, Nikolaos Chatzipanagiotis, Michael M ZavlanosAbstract:In this paper, we present complexity certification results for a distributed augmented Lagrangian (AL) algorithm used to solve convex optimization problems involving globally coupled linear constraints. Our method relies on the accelerated distributed AL (ADAL) algorithm, which can handle the coupled linear constraints in a distributed manner based on local estimates of the AL. We show that the theoretical complexity of ADAL to reach an $\epsilon$ -optimal solution both in terms of suboptimality and infeasibility is $O(\frac{1}{\epsilon })$ iterations. Moreover, we provide a valid upper bound for the optimal Dual Multiplier, which enables us to explicitly specify these complexity bounds. We also show how to choose the step-size parameter to minimize the bounds on the convergence rates. Finally, we discuss a motivating example, a model predictive control problem, involving a finite number of subsystems, which interact with each other via a general network.
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complexity certification of a distributed augmented lagrangian method
arXiv: Optimization and Control, 2017Co-Authors: Soomin Lee, Nikolaos Chatzipanagiotis, Michael M ZavlanosAbstract:In this paper we present complexity certification results for a distributed Augmented Lagrangian (AL) algorithm used to solve convex optimization problems involving globally coupled linear constraints. Our method relies on the Accelerated Distributed Augmented Lagrangian (ADAL) algorithm, which can handle the coupled linear constraints in a distributed manner based on local estimates of the AL. We show that the theoretical complexity of ADAL to reach an $\epsilon$-optimal solution both in terms of suboptimality and infeasibility is $O(\frac{1}{\epsilon})$ iterations. Moreover, we provide a valid upper bound for the optimal Dual Multiplier which enables us to explicitly specify these complexity bounds. We also show how to choose the stepsize parameter to minimize the bounds on the convergence rates. Finally, we discuss a motivating example, a model predictive control (MPC) problem, involving a finite number of subsystems which interact with each other via a general network.
Nikolaos Chatzipanagiotis - One of the best experts on this subject based on the ideXlab platform.
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complexity certification of a distributed augmented lagrangian method
IEEE Transactions on Automatic Control, 2018Co-Authors: Soomin Lee, Nikolaos Chatzipanagiotis, Michael M ZavlanosAbstract:In this paper, we present complexity certification results for a distributed augmented Lagrangian (AL) algorithm used to solve convex optimization problems involving globally coupled linear constraints. Our method relies on the accelerated distributed AL (ADAL) algorithm, which can handle the coupled linear constraints in a distributed manner based on local estimates of the AL. We show that the theoretical complexity of ADAL to reach an $\epsilon$ -optimal solution both in terms of suboptimality and infeasibility is $O(\frac{1}{\epsilon })$ iterations. Moreover, we provide a valid upper bound for the optimal Dual Multiplier, which enables us to explicitly specify these complexity bounds. We also show how to choose the step-size parameter to minimize the bounds on the convergence rates. Finally, we discuss a motivating example, a model predictive control problem, involving a finite number of subsystems, which interact with each other via a general network.
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complexity certification of a distributed augmented lagrangian method
arXiv: Optimization and Control, 2017Co-Authors: Soomin Lee, Nikolaos Chatzipanagiotis, Michael M ZavlanosAbstract:In this paper we present complexity certification results for a distributed Augmented Lagrangian (AL) algorithm used to solve convex optimization problems involving globally coupled linear constraints. Our method relies on the Accelerated Distributed Augmented Lagrangian (ADAL) algorithm, which can handle the coupled linear constraints in a distributed manner based on local estimates of the AL. We show that the theoretical complexity of ADAL to reach an $\epsilon$-optimal solution both in terms of suboptimality and infeasibility is $O(\frac{1}{\epsilon})$ iterations. Moreover, we provide a valid upper bound for the optimal Dual Multiplier which enables us to explicitly specify these complexity bounds. We also show how to choose the stepsize parameter to minimize the bounds on the convergence rates. Finally, we discuss a motivating example, a model predictive control (MPC) problem, involving a finite number of subsystems which interact with each other via a general network.
Inmaculada Sirvent - One of the best experts on this subject based on the ideXlab platform.
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choosing weights from alternative optimal solutions of Dual Multiplier models in dea
European Journal of Operational Research, 2007Co-Authors: W W Cooper, Jose L Ruiz, Inmaculada SirventAbstract:In this paper we propose a two-step procedure to be used for the selection of the weights that we obtain from the Multiplier model in a DEA efficiency analysis. It is well known that optimal solutions of the envelopment formulation for extreme efficient units are often highly degenerate and, consequently, have alternate optima for the weights. Different optimal weights may then be obtained depending, for instance, on the software used. The idea behind the procedure we present is to explore the set of alternate optima in order to help make a choice of optimal weights. The selection of weights for a given extreme efficient point is connected with the dimension of the efficient facets of the frontier. Our approach makes it possible to select the weights associated with the facets of higher dimension that this unit generates and, in particular, it selects those weights associated with a full dimensional efficient facet (FDEF) if any. In this sense the weights provided by our procedure will have the maximum support from the production possibility set. We also look for weights that maximize the relative value of the inputs and outputs included in the efficiency analysis in a sense to be described in this article.
W W Cooper - One of the best experts on this subject based on the ideXlab platform.
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choosing weights from alternative optimal solutions of Dual Multiplier models in dea
European Journal of Operational Research, 2007Co-Authors: W W Cooper, Jose L Ruiz, Inmaculada SirventAbstract:In this paper we propose a two-step procedure to be used for the selection of the weights that we obtain from the Multiplier model in a DEA efficiency analysis. It is well known that optimal solutions of the envelopment formulation for extreme efficient units are often highly degenerate and, consequently, have alternate optima for the weights. Different optimal weights may then be obtained depending, for instance, on the software used. The idea behind the procedure we present is to explore the set of alternate optima in order to help make a choice of optimal weights. The selection of weights for a given extreme efficient point is connected with the dimension of the efficient facets of the frontier. Our approach makes it possible to select the weights associated with the facets of higher dimension that this unit generates and, in particular, it selects those weights associated with a full dimensional efficient facet (FDEF) if any. In this sense the weights provided by our procedure will have the maximum support from the production possibility set. We also look for weights that maximize the relative value of the inputs and outputs included in the efficiency analysis in a sense to be described in this article.
