University of Guilan Journal of Mathematical Modeling 2345-394X 11 1 2023 03 01 Applications of the proximal difference-of-convex algorithm with extrapolation in optimal correction 35 54 5899 10.22124/jmm.2022.22498.1986 EN Samira Shahsavari Department of Applied Mathematics, Faculty of Mathematical Sciences University of Guilan, Rasht, Iran Saeed Ketabchi Department of Applied Mathematics, Faculty of Mathematical Sciences University of Guilan, Rasht, Iran Journal Article 2022 06 15 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. https://jmm.guilan.ac.ir/article_5899_66338635390d14bd52c966e73943f022.pdf