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DC programming and DCA for solving Brugnano–Casulli piecewise linear systems
- Source :
- Computers and Operations Research, Computers and Operations Research, Elsevier, 2017, 87, pp.196-204. ⟨10.1016/j.cor.2016.04.005⟩
- Publication Year :
- 2017
- Publisher :
- HAL CCSD, 2017.
-
Abstract
- Piecewise linear optimization is one of the most frequently used optimization models in practice, such as transportation, finance and supply-chain management. In this paper, we investigate a particular piecewise linear optimization that is optimizing the norm of piecewise linear functions (NPLF). Specifically, we are interested in solving a class of Brugnano–Casulli piecewise linear systems (PLS), which can be reformulated as an NPLF problem. Speaking generally, the NPLF is considered as an optimization problem with a nonsmooth, nonconvex objective function. A new and efficient optimization approach based on DC (Difference of Convex functions) programming and DCA (DC Algorithms) is developed. With a suitable DC formulation, we design a DCA scheme, named l1-DCA, for the problem of optimizing the l1-norm of NPLF. Thanks to particular properties of the problem, we prove that under some conditions, our proposed algorithm converges to an exact solution after a finite number of iterations. In addition, when a nonglobal solution is found, a numerical procedure is introduced to find a feasible point having a smaller objective value and to restart l1-DCA at this point. Several numerical experiments illustrate these interesting convergence properties. Moreover, we also present an application to the free-surface hydrodynamic problem, where the correct numerical modeling often requires to have the solution of special PLS, with the aim of showing the efficiency of the proposed method.
- Subjects :
- Mathematical optimization
021103 operations research
Optimization problem
General Computer Science
0211 other engineering and technologies
010103 numerical & computational mathematics
02 engineering and technology
Management Science and Operations Research
01 natural sciences
Linear-fractional programming
Piecewise linear function
Exact solutions in general relativity
Modeling and Simulation
Convergence (routing)
Point (geometry)
[INFO]Computer Science [cs]
0101 mathematics
Convex function
Finite set
ComputingMilieux_MISCELLANEOUS
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 03050548
- Database :
- OpenAIRE
- Journal :
- Computers and Operations Research, Computers and Operations Research, Elsevier, 2017, 87, pp.196-204. ⟨10.1016/j.cor.2016.04.005⟩
- Accession number :
- edsair.doi.dedup.....601eecbf54bab1591b023acc48c90ece