Calmness of partially perturbed linear systems with an application to the central path
- Cánovas, Maria, Hall, Julian, López, Marco, Parra, Juan
- Authors: Cánovas, Maria , Hall, Julian , López, Marco , Parra, Juan
- Date: 2019
- Type: Text , Journal article
- Relation: Optimization Vol. 68, no. 2-3 (2019), p. 465-483
- Full Text:
- Reviewed:
- Description: In this paper we develop point-based formulas for the calmness modulus of the feasible set mapping in the context of linear inequality systems with a fixed abstract constraint and (partially) perturbed linear constraints. The case of totally perturbed linear systems was previously analyzed in [Canovas MJ, Lopez MA, Parra J, et al. Calmness of the feasible set mapping for linear inequality systems. Set-Valued Var Anal. 2014;22:375-389, Section 5]. We point out that the presence of such an abstract constraint yields the current paper to appeal to a notable different methodology with respect to previous works on the calmness modulus in linear programming. The interest of this model comes from the fact that partially perturbed systems naturally appear in many applications. As an illustration, the paper includes an example related to the classical central path construction. In this example we consider a certain feasible set mapping whose calmness modulus provides a measure of the convergence of the central path. Finally, we underline the fact that the expression for the calmness modulus obtained in this paper is (conceptually) implementable as far as it only involves the nominal data.
- Authors: Cánovas, Maria , Hall, Julian , López, Marco , Parra, Juan
- Date: 2019
- Type: Text , Journal article
- Relation: Optimization Vol. 68, no. 2-3 (2019), p. 465-483
- Full Text:
- Reviewed:
- Description: In this paper we develop point-based formulas for the calmness modulus of the feasible set mapping in the context of linear inequality systems with a fixed abstract constraint and (partially) perturbed linear constraints. The case of totally perturbed linear systems was previously analyzed in [Canovas MJ, Lopez MA, Parra J, et al. Calmness of the feasible set mapping for linear inequality systems. Set-Valued Var Anal. 2014;22:375-389, Section 5]. We point out that the presence of such an abstract constraint yields the current paper to appeal to a notable different methodology with respect to previous works on the calmness modulus in linear programming. The interest of this model comes from the fact that partially perturbed systems naturally appear in many applications. As an illustration, the paper includes an example related to the classical central path construction. In this example we consider a certain feasible set mapping whose calmness modulus provides a measure of the convergence of the central path. Finally, we underline the fact that the expression for the calmness modulus obtained in this paper is (conceptually) implementable as far as it only involves the nominal data.
Two curve Chebyshev approximation and its application to signal clustering
- Authors: Sukhorukova, Nadezda
- Date: 2019
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 356, no. (2019), p. 42-49
- Relation: http://purl.org/au-research/grants/arc/DP180100602
- Full Text:
- Reviewed:
- Description: In this paper, we extend a number of important results of the classical Chebyshev approximation theory to the case of simultaneous approximation of two or more functions. The need for this extension is application driven, since such kind of problems appears in the area of curve (signal) clustering. In this paper, we propose a new efficient algorithm for signal clustering and develop a procedure that allows one to reuse the results obtained at the previous iteration without recomputing the cluster centres from scratch. This approach is based on the extension of the classical de la Vallee-Poussin procedure originally developed for polynomial approximation. We also develop necessary and sufficient optimality conditions for two curve Chebyshev approximation, which is our core tool for curve clustering. These results are based on application of nonsmooth convex analysis. (C) 2019 Elsevier Inc. All rights reserved. In this paper, we extend a number of important results of the classical Chebyshev approximation theory to the case of simultaneous approximation of two or more functions. The need for this extension is application driven, since such kind of problems appears in the area of curve (signal) clustering. In this paper, we propose a new efficient algorithm for signal clustering and develop a procedure that allows one to reuse the results obtained at the previous iteration without recomputing the cluster centres from scratch. This approach is based on the extension of the classical de la Vallee-Poussin procedure originally developed for polynomial approximation. We also develop necessary and sufficient optimality conditions for two curve Chebyshev approximation, which is our core tool for curve clustering. These results are based on application of nonsmooth convex analysis. (C) 2019 Elsevier Inc. All rights reserved.
- Authors: Sukhorukova, Nadezda
- Date: 2019
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 356, no. (2019), p. 42-49
- Relation: http://purl.org/au-research/grants/arc/DP180100602
- Full Text:
- Reviewed:
- Description: In this paper, we extend a number of important results of the classical Chebyshev approximation theory to the case of simultaneous approximation of two or more functions. The need for this extension is application driven, since such kind of problems appears in the area of curve (signal) clustering. In this paper, we propose a new efficient algorithm for signal clustering and develop a procedure that allows one to reuse the results obtained at the previous iteration without recomputing the cluster centres from scratch. This approach is based on the extension of the classical de la Vallee-Poussin procedure originally developed for polynomial approximation. We also develop necessary and sufficient optimality conditions for two curve Chebyshev approximation, which is our core tool for curve clustering. These results are based on application of nonsmooth convex analysis. (C) 2019 Elsevier Inc. All rights reserved. In this paper, we extend a number of important results of the classical Chebyshev approximation theory to the case of simultaneous approximation of two or more functions. The need for this extension is application driven, since such kind of problems appears in the area of curve (signal) clustering. In this paper, we propose a new efficient algorithm for signal clustering and develop a procedure that allows one to reuse the results obtained at the previous iteration without recomputing the cluster centres from scratch. This approach is based on the extension of the classical de la Vallee-Poussin procedure originally developed for polynomial approximation. We also develop necessary and sufficient optimality conditions for two curve Chebyshev approximation, which is our core tool for curve clustering. These results are based on application of nonsmooth convex analysis. (C) 2019 Elsevier Inc. All rights reserved.
Calmness modulus of linear semi-infinite programs
- Cánovas, Maria, Kruger, Alexander, López, Marco, Parra, Juan, Théra, Michel
- Authors: Cánovas, Maria , Kruger, Alexander , López, Marco , Parra, Juan , Théra, Michel
- Date: 2014
- Type: Text , Journal article
- Relation: SIAM Journal on Optimization Vol. 24, no. 1 (2014), p. 29-48
- Relation: http://purl.org/au-research/grants/arc/DP110102011
- Full Text:
- Reviewed:
- Description: Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.
- Authors: Cánovas, Maria , Kruger, Alexander , López, Marco , Parra, Juan , Théra, Michel
- Date: 2014
- Type: Text , Journal article
- Relation: SIAM Journal on Optimization Vol. 24, no. 1 (2014), p. 29-48
- Relation: http://purl.org/au-research/grants/arc/DP110102011
- Full Text:
- Reviewed:
- Description: Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.
An extended lifetime measure for telecommunications networks : Improvements and implementations
- Dzalilov, Zari, Ouveysi, Iradj, Bektas, Tolga
- Authors: Dzalilov, Zari , Ouveysi, Iradj , Bektas, Tolga
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 8, no. 3 (2012), p. 639-649
- Full Text:
- Reviewed:
- Description: Predicting the lifetime of a network is a stochastic and very hard task. Sensitivity analysis of a network in order to identify the weakest points in the network, provides valuable knowledge to draw an optimum investment strategy for the expansion of the networks for the network carriers. To achieve this goal, a new measure, called topology lifetime, was recently proposed for measuring the performance of a telecommunication network. This measure not only allows to perform a sensitivity analysis of the networks, but also it provides the means to compare the different topologies with respect to the ability of the network in supporting growth in network traffic before new capacity/facility is installed. This paper addresses some improvements upon the previously defined measures and presents the implementation results of the various lifetime measure methodologies. Computational analysis on some commonly used topologies show how the new measure can be utilized in assessing network performance.
- Description: 2003010401
- Authors: Dzalilov, Zari , Ouveysi, Iradj , Bektas, Tolga
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 8, no. 3 (2012), p. 639-649
- Full Text:
- Reviewed:
- Description: Predicting the lifetime of a network is a stochastic and very hard task. Sensitivity analysis of a network in order to identify the weakest points in the network, provides valuable knowledge to draw an optimum investment strategy for the expansion of the networks for the network carriers. To achieve this goal, a new measure, called topology lifetime, was recently proposed for measuring the performance of a telecommunication network. This measure not only allows to perform a sensitivity analysis of the networks, but also it provides the means to compare the different topologies with respect to the ability of the network in supporting growth in network traffic before new capacity/facility is installed. This paper addresses some improvements upon the previously defined measures and presents the implementation results of the various lifetime measure methodologies. Computational analysis on some commonly used topologies show how the new measure can be utilized in assessing network performance.
- Description: 2003010401
An extended lifetime measure for telecommunication network
- Dzalilov, Zari, Ouveysi, Iradj, Rubinov, Alex
- Authors: Dzalilov, Zari , Ouveysi, Iradj , Rubinov, Alex
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 4, no. 2 (2008), p. 329-337
- Full Text:
- Reviewed:
- Description: A new measure for network performance evaluation called topology lifetime was introduced in [4, 5]. This measure is based on the notion of unexpected traffic growth and can be used for comparison of topologies. We discuss some advantages and disadvantages of the approach of [4] and suggest some modifications to this approach. In particular we discuss how to evaluate the influence of a subgraph to the lifetime measure and introduce the notion of the order of a path. This notion is useful if we consider a possible extension to the set of working paths in order to support the traffic for the time that is needed for installation of new facilities.
- Authors: Dzalilov, Zari , Ouveysi, Iradj , Rubinov, Alex
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of Industrial and Management Optimization Vol. 4, no. 2 (2008), p. 329-337
- Full Text:
- Reviewed:
- Description: A new measure for network performance evaluation called topology lifetime was introduced in [4, 5]. This measure is based on the notion of unexpected traffic growth and can be used for comparison of topologies. We discuss some advantages and disadvantages of the approach of [4] and suggest some modifications to this approach. In particular we discuss how to evaluate the influence of a subgraph to the lifetime measure and introduce the notion of the order of a path. This notion is useful if we consider a possible extension to the set of working paths in order to support the traffic for the time that is needed for installation of new facilities.
- «
- ‹
- 1
- ›
- »