This paper proposes a proximal difference-of-convex algorithm with extrapolation ($PDCA_e$) based on Dinkelbach's approach for the optimal correction of two types of piecewise linear systems, classical obstacle problems and equilibrium problems, and linear inequalities. Using Dinkelbach's theorem leads to getting the roots of two single-variable functions. Considering the non-convex and level-bounded properties of the obtained problems, we use a proximal difference-of-convex algorithm programming to solve them. The experimental results on several randomly generated test problems show that the $PDCA_e$-generalized Newton method outperforms other methods for both feasible and infeasible cases.
Shahsavari, S., & Ketabchi, S. (2023). Applications of the proximal difference-of-convex algorithm with extrapolation in optimal correction. Journal of Mathematical Modeling, 11(1), 35-54. doi: 10.22124/jmm.2022.22498.1986
MLA
Samira Shahsavari; Saeed Ketabchi. "Applications of the proximal difference-of-convex algorithm with extrapolation in optimal correction". Journal of Mathematical Modeling, 11, 1, 2023, 35-54. doi: 10.22124/jmm.2022.22498.1986
HARVARD
Shahsavari, S., Ketabchi, S. (2023). 'Applications of the proximal difference-of-convex algorithm with extrapolation in optimal correction', Journal of Mathematical Modeling, 11(1), pp. 35-54. doi: 10.22124/jmm.2022.22498.1986
VANCOUVER
Shahsavari, S., Ketabchi, S. Applications of the proximal difference-of-convex algorithm with extrapolation in optimal correction. Journal of Mathematical Modeling, 2023; 11(1): 35-54. doi: 10.22124/jmm.2022.22498.1986
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