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5López, Marco
4Cánovas, Maria
4Parra, Juan
2Dzalilov, Zari
2Ouveysi, Iradj
2Sukhorukova, Nadezda
1Akbar, Mariam
1Bektas, Tolga
1Goberna, Miguel
1Gunawan, Indra
1Hall, Julian
1He, Xing
1Huang, Junjian
1Huang, Tingwen
1Ibrahim, Yousef
1Imran, Muhammad
1Javaid, Nadeem
1Korshidi, Hadi
1Kruger, Alexander
1Li, Chaojie

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60103 Numerical and Computational Mathematics
50102 Applied Mathematics
20101 Pure Mathematics
2Calmness
2Feasible set mapping
2Local error bounds
2Nonsmooth analysis
2Optimization
2Semi-infinite programming
2Variational analysis
10802 Computation Theory and Mathematics
14006 Communications engineering
14606 Distributed computing and systems software
1Bilevel linear programming
1Bilevel linear programming problem (BLPP)
1Calmness modulus
1Chain distribution
1Chebyshev approximation
1Computer science

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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.

Workload coverage through nonsmooth optimization

- Sukhorukova, Nadezda, Ugon, Julien, Yearwood, John

**Authors:**Sukhorukova, Nadezda , Ugon, Julien , Yearwood, John**Date:**2009**Type:**Text , Journal article**Relation:**Optimization Methods and Software Vol. 24, no. 2 (2009), p. 285-298**Full Text:**false**Reviewed:****Description:**In this paper, workload coverage is the problem of identifying a pattern of days worked and days off, along with the number of hours worked on each work day. This pattern must satisfy certain work-related constraints and fit best to a predefined workload. In our study, we formulate the problem of workload coverage as an optimization problem. We propose a number of models which take into consideration various staffing constraints. For each of these models, our study aims to find a compromise between an accurate workload coverage and the ability to solve the corresponding optimization problems in a reasonable time. Numerical experiments on each model are carried out and the results are presented. Interestingly, the nonlinear programming approaches are found to be competitive with linear programming ones. © 2009 Taylor & Francis.

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

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.

Calmness of the feasible set mapping for linear inequality systems

- Cánovas, Maria, López, Marco, Parra, Juan, Toledo, Javier

**Authors:**Cánovas, Maria , López, Marco , Parra, Juan , Toledo, Javier**Date:**2014**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 22, no. 2 (2014), p. 375-389**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:**false**Reviewed:****Description:**In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system's data.

A recurrent neural network for solving bilevel linear programming problem

- He, Xing, Li, Chuandong, Huang, Tingwen, Li, Chaojie, Huang, Junjian

**Authors:**He, Xing , Li, Chuandong , Huang, Tingwen , Li, Chaojie , Huang, Junjian**Date:**2014**Type:**Text , Journal article**Relation:**IEEE Transactions on Neural Networks and Learning Systems Vol. 25, no. 4 (April 2014 2014), p. 824-830**Full Text:**false**Reviewed:****Description:**In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.

An optimization model for multi-state weighted kout-of-n system reliability value

- Korshidi, Hadi, Gunawan, Indra, Ibrahim, Yousef

**Authors:**Korshidi, Hadi , Gunawan, Indra , Ibrahim, Yousef**Date:**2013**Type:**Text , Conference proceedings**Relation:**IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society, Vienna, Austria Nov. 2013, p.4357-4361**Full Text:**false**Reviewed:****Description:**A reliability optimization model is proposed in this paper for multi-state weighted k-out-of-n systems. In this model, income generated by components through each functioning period is used as a reliability index. Therefore, time value of money is used in the presented optimization model to estimate both system's reliability and cost. The system reliability is evaluated by Universal Generating Function (UGF). The model's objective function is to maximize the net present value (NPV) of the system. Therefore, it would maximize the system reliability and minimize the system cost simultaneously. A numerical example is presented in this paper to illustrate the model by finding the optimal design of the system, and the best time for maintenance plan. Also, a discussion is provided based on the result.

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**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**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.

A note on primal-dual stability in infinite linear programming

- Goberna, Miguel, López, Marco, Ridolfi, Andrea, Vera de Serio, Virginia

**Authors:**Goberna, Miguel , López, Marco , Ridolfi, Andrea , Vera de Serio, Virginia**Date:**2020**Type:**Text , Journal article**Relation:**Optimization Letters Vol. 14, no. 8 (2020), p. 2247-2263**Full Text:**false**Reviewed:****Description:**In this note we analyze the simultaneous preservation of the consistency (and of the inconsistency) of linear programming problems posed in infinite dimensional Banach spaces, and their corresponding dual problems, under sufficiently small perturbations of the data. We consider seven different scenarios associated with the different possibilities of perturbations of the data (the objective functional, the constraint functionals, and the right hand-side function), i.e., which of them are known, and remain fixed, and which ones can be perturbed because of their uncertainty. The obtained results allow us to give sufficient and necessary conditions for the coincidence of the optimal values of both problems and for the stability of the duality gap under the same type of perturbations. There appear substantial differences with the finite dimensional case due to the distinct topological properties of cones in finite and infinite dimensional Banach spaces. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.**Description:**Funding details: Australian Research Council, ARC, DP180100602: http://purl.org/au-research/grants/arc/DP180100602

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.

Subdifferentials and stability analysis of feasible set and pareto front mappings in linear multiobjective optimization

- Cánovas, Maria, López, Marco, Mordukhovich, Boris, Parra, Juan

**Authors:**Cánovas, Maria , López, Marco , Mordukhovich, Boris , Parra, Juan**Date:**2020**Type:**Text , Journal article**Relation:**Vietnam Journal of Mathematics Vol. 48, no. 2 (2020), p. 315-334**Full Text:****Reviewed:****Description:**The paper concerns multiobjective linear optimization problems in**Description:**Funding details: European Commission, EC Funding details: European Regional Development Fund, FEDER Funding details: Australian Research Council, ARC Funding details: Australian Research Council, ARC, DP180100602 Funding details: Australian Research Council, ARC, DP-190100555 Funding details: Air Force Office of Scientific Research, AFOSR, 15RT04 Funding details: DMS-1512846, DMS-1808978 Funding text 1: This research has been partially supported by grants MTM2014-59179-C2-(1,2)-P and PGC2018-097960-B-C2(1,2) from MINECO/MICINN, Spain, and ERDF, “A way to make Europe”, European Union. Funding text 2: Research of the second author is also partially supported by the Australian Research Council (ARC) Discovery Grants Scheme (Project Grant # DP180100602). Funding text 3: Research of third author was partially supported by the USA National Science Foundation under grants DMS-1512846 and DMS-1808978, by the USA Air Force Office of Scientific Research grant #15RT04, and by Australian Research Council under grant DP-190100555.

**Authors:**Cánovas, Maria , López, Marco , Mordukhovich, Boris , Parra, Juan**Date:**2020**Type:**Text , Journal article**Relation:**Vietnam Journal of Mathematics Vol. 48, no. 2 (2020), p. 315-334**Full Text:****Reviewed:****Description:**The paper concerns multiobjective linear optimization problems in**Description:**Funding details: European Commission, EC Funding details: European Regional Development Fund, FEDER Funding details: Australian Research Council, ARC Funding details: Australian Research Council, ARC, DP180100602 Funding details: Australian Research Council, ARC, DP-190100555 Funding details: Air Force Office of Scientific Research, AFOSR, 15RT04 Funding details: DMS-1512846, DMS-1808978 Funding text 1: This research has been partially supported by grants MTM2014-59179-C2-(1,2)-P and PGC2018-097960-B-C2(1,2) from MINECO/MICINN, Spain, and ERDF, “A way to make Europe”, European Union. Funding text 2: Research of the second author is also partially supported by the Australian Research Council (ARC) Discovery Grants Scheme (Project Grant # DP180100602). Funding text 3: Research of third author was partially supported by the USA National Science Foundation under grants DMS-1512846 and DMS-1808978, by the USA Air Force Office of Scientific Research grant #15RT04, and by Australian Research Council under grant DP-190100555.

A multi-hop angular routing protocol for wireless sensor networks

- Akbar, Mariam, Javaid, Nadeem, Imran, Muhammad, Rao, Areeba, Younis, Muhammad, Niaz, Iftikhar

**Authors:**Akbar, Mariam , Javaid, Nadeem , Imran, Muhammad , Rao, Areeba , Younis, Muhammad , Niaz, Iftikhar**Date:**2016**Type:**Text , Journal article**Relation:**International Journal of Distributed Sensor Networks Vol. 12, no. 9 (2016), p.**Full Text:****Reviewed:****Description:**In this article, we propose two new routing protocols for wireless sensor networks. First one is AM-DisCNT (angular multi-hop distance-based clustering network transmission) protocol which uses circular deployment of sensors (nodes) for uniform energy consumption in the network. The protocol operates in such a way that nodes with maximum residual energy are selected as cluster heads for each round. Second one is iAM-DisCNT (improved AM-DisCNT) protocol which exploits both mobile and static base stations for throughput maximization. Besides the proposition of routing protocols, iAM-DisCNT is provided with three mathematical models: two linear-programming-based models for information flow maximization and packet drop rate minimization and one model for calculating energy consumption of nodes. Graphical analysis for linear-programming-based mathematical formulation is also part of this work. Simulation results show that AM-DisCNT has 32% and iAM-DisCNT has 48% improved stability period as compared to LEACH (low-energy adaptive clustering hierarchy) and DEEC (distributed energy-efficient clustering) routing protocols. Similarly, throughput of AM-DisCNT and iAM-DisCNT is improved by 16% and 80%, respectively, in comparison with the counterpart schemes. © The Author(s) 2016.

**Authors:**Akbar, Mariam , Javaid, Nadeem , Imran, Muhammad , Rao, Areeba , Younis, Muhammad , Niaz, Iftikhar**Date:**2016**Type:**Text , Journal article**Relation:**International Journal of Distributed Sensor Networks Vol. 12, no. 9 (2016), p.**Full Text:****Reviewed:****Description:**In this article, we propose two new routing protocols for wireless sensor networks. First one is AM-DisCNT (angular multi-hop distance-based clustering network transmission) protocol which uses circular deployment of sensors (nodes) for uniform energy consumption in the network. The protocol operates in such a way that nodes with maximum residual energy are selected as cluster heads for each round. Second one is iAM-DisCNT (improved AM-DisCNT) protocol which exploits both mobile and static base stations for throughput maximization. Besides the proposition of routing protocols, iAM-DisCNT is provided with three mathematical models: two linear-programming-based models for information flow maximization and packet drop rate minimization and one model for calculating energy consumption of nodes. Graphical analysis for linear-programming-based mathematical formulation is also part of this work. Simulation results show that AM-DisCNT has 32% and iAM-DisCNT has 48% improved stability period as compared to LEACH (low-energy adaptive clustering hierarchy) and DEEC (distributed energy-efficient clustering) routing protocols. Similarly, throughput of AM-DisCNT and iAM-DisCNT is improved by 16% and 80%, respectively, in comparison with the counterpart schemes. © The Author(s) 2016.

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