Description:
In this paper, we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in Bonnans and Ramirez [Perturbation analysis of second-order cone programming problems, Math Program. 2005;104(2-30):205-227] for conic optimization problems, and in Pena and Roshchina [A complementarity partition theorem for multifold conic systems, Math Program. 2013;142(1-2):579-589] for homogeneous feasibility problems. We show that both can be treated within the same unified geometric framework and extend the latter notion to optimization problems. We also show that the two partitions do not coincide, and their intersection gives a seven-set index partition. Finally, we demonstrate that the partitions are preserved under the application of nonsingular linear transformations, and in particular, that a standard conversion of a second-order cone program into a semidefinite programming problem preserves the partitions.
Description:
This research was partially supported by ANID (Chile) under REDES project number 180032 and by the Australian Research Council grant DE150100240. The second author was supported by FONDECYT (Fondo de Fomento al Desarrollo Cientifico y Tecnologico) regular projects 1160204 and 1201982, and Basal Program CMM-AFB 170001 (Comision Nacional de Investigacion Cientifica y Tecnologica), all from ANID (Chile).
Description:
In this paper, we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in Bonnans and Ramirez [Perturbation analysis of second-order cone programming problems, Math Program. 2005;104(2-30):205-227] for conic optimization problems, and in Pena and Roshchina [A complementarity partition theorem for multifold conic systems, Math Program. 2013;142(1-2):579-589] for homogeneous feasibility problems. We show that both can be treated within the same unified geometric framework and extend the latter notion to optimization problems. We also show that the two partitions do not coincide, and their intersection gives a seven-set index partition. Finally, we demonstrate that the partitions are preserved under the application of nonsingular linear transformations, and in particular, that a standard conversion of a second-order cone program into a semidefinite programming problem preserves the partitions.
Description:
This research was partially supported by ANID (Chile) under REDES project number 180032 and by the Australian Research Council grant DE150100240. The second author was supported by FONDECYT (Fondo de Fomento al Desarrollo Cientifico y Tecnologico) regular projects 1160204 and 1201982, and Basal Program CMM-AFB 170001 (Comision Nacional de Investigacion Cientifica y Tecnologica), all from ANID (Chile).
Description:
The authors extend their appreciation to the International Scientific Partnership Program ISPP at King Saud University for funding this research work through ISPP-78. This work is partially supported by China Postdoctoral Science Foundation ( 2019M651115 ).
Description:
The authors extend their appreciation to the International Scientific Partnership Program ISPP at King Saud University for funding this research work through ISPP-78. This work is partially supported by China Postdoctoral Science Foundation ( 2019M651115 ).
Description:
A new global optimization method combining genetic algorithm and Hooke-Jeeves method to solve a class of constrained optimization problems is studied in this paper. We first introduce the quadratic penalty function method and the exact penalty function method to transform the original constrained optimization problem with general equality and inequality constraints into a sequence of optimization problems only with box constraints. Then, the combination of genetic algorithm and Hooke-Jeeves method is applied to solve the transformed optimization problems. Since Hooke-Jeeves method is good at local search, our proposed method dramatically improves the accuracy and convergence rate of genetic algorithm. In view of the derivative-free of Hooke-Jeeves method, our method only requires information of objective function value which not only can overcome the computational difficulties caused by the ill-condition of the square penalty function, but also can handle the non-diffierentiability by the exact penalty function. Some well-known test problems are investigated. The numerical results show that our proposed method is eficient and robust.
Description:
A new global optimization method combining genetic algorithm and Hooke-Jeeves method to solve a class of constrained optimization problems is studied in this paper. We first introduce the quadratic penalty function method and the exact penalty function method to transform the original constrained optimization problem with general equality and inequality constraints into a sequence of optimization problems only with box constraints. Then, the combination of genetic algorithm and Hooke-Jeeves method is applied to solve the transformed optimization problems. Since Hooke-Jeeves method is good at local search, our proposed method dramatically improves the accuracy and convergence rate of genetic algorithm. In view of the derivative-free of Hooke-Jeeves method, our method only requires information of objective function value which not only can overcome the computational difficulties caused by the ill-condition of the square penalty function, but also can handle the non-diffierentiability by the exact penalty function. Some well-known test problems are investigated. The numerical results show that our proposed method is eficient and robust.
Description:
The research was supported by the Australian Research Council, Project DP160100854, and the European Union’s Horizon 2020 research and innovation programme under the Marie Sk
Description:
The research was supported by the Australian Research Council, Project DP160100854, and the European Union’s Horizon 2020 research and innovation programme under the Marie Sk
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.
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.
Description:
This research was supported by the Australian Research Council (ARC), Solving hard Chebyshev approximation problems through nonsmooth analysis (Discovery Project DP180100602 ). This research was partially sponsored by Tel Aviv-Swinburne Research Collaboration Grant (2019).