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20102 Applied Mathematics
20103 Numerical and Computational Mathematics
2Optimization
10906 Electrical and Electronic Engineering
1Calmness modulus
1Clusterwise linear regression
1Clusterwise linear regressions
1Computer science
1Constrained problem
1DC optimization
1Difference of convex algorithms
1Engineering economics
1Engineering industries
1Fault tolerant systems
1Function evaluation
1Functions
1Incremental approach
1Isolated calmness
1Linear programming

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Incremental DC optimization algorithm for large-scale clusterwise linear regression

- Bagirov, Adil, Taheri, Sona, Cimen, Emre

**Authors:**Bagirov, Adil , Taheri, Sona , Cimen, Emre**Date:**2021**Type:**Text , Journal article**Relation:**Journal of Computational and Applied Mathematics Vol. 389, no. (2021), p. 1-17**Relation:**https://purl.org/au-research/grants/arc/DP190100580**Full Text:**false**Reviewed:****Description:**The objective function in the nonsmooth optimization model of the clusterwise linear regression (CLR) problem with the squared regression error is represented as a difference of two convex functions. Then using the difference of convex algorithm (DCA) approach the CLR problem is replaced by the sequence of smooth unconstrained optimization subproblems. A new algorithm based on the DCA and the incremental approach is designed to solve the CLR problem. We apply the Quasi-Newton method to solve the subproblems. The proposed algorithm is evaluated using several synthetic and real-world data sets for regression and compared with other algorithms for CLR. Results demonstrate that the DCA based algorithm is efficient for solving CLR problems with the large number of data points and in particular, outperforms other algorithms when the number of input variables is small. © 2020 Elsevier B.V.

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.

A bi-objective dynamic model for multi-state weighted k-out-of-n system reliability

- Khorshidi, Hadi, Gunawan, Indra, Ibrahim, Yousef

**Authors:**Khorshidi, Hadi , Gunawan, Indra , Ibrahim, Yousef**Date:**2015**Type:**Text , Conference paper**Relation:**25th European Safety and Reliability Conference, ESREL 2015; Zurich, Switzerland; 7th-10th September 2015 p. 2229-2234**Full Text:**false**Reviewed:****Description:**Nowadays, improving system reliability is becoming an important criterion for engineering industries. Many studies have been developed to evaluate the reliability of the systems which is the first step in system improvement. Most of these studies have been done in non-dynamic conditions in which the components have the constant reliability values during functioning periods. However, the components' reliability level varies over time due to both failures and maintenance actions. Therefore, time dimension should be added into system reliability evaluation. In this paper, a dynamic assessment is presented for multi-state weighted k-out-of-n systems. The k-out-of-n system is a popular structure in fault-tolerant systems in which n components work in parallel form with a pre-defined k as a condition. This dynamic assessment considers the reliability variation of the components over finite and discrete time periods. It provides an opportunity to assign decision variables for each functioning period, and analyze the impact of each decision on the whole system reliability. In addition, the income generated during each period is defined as an importance weight of the components. Therefore, the present value of the system is obtained by Universal Generating Function (UGF) and engineering economics' tools. Furthermore, an optimization model is developed to find optimal decisions based on system reliability and cost. Since the system reliability is estimated by money, the expected profit of the system can be as the objective function. As a result, the objective function can maximize system reliability and minimize system cost simultaneously. A Matlab programming is created for a numerical example to illustrate the proposed model. © 2015 Taylor & Francis Group, London.

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