University of GuilanJournal of Mathematical Modeling2345-394X11120230301Applications of the proximal difference-of-convex algorithm with extrapolation in optimal correction3554589910.22124/jmm.2022.22498.1986ENSamiraShahsavariDepartment of Applied Mathematics, Faculty of Mathematical Sciences University of Guilan, Rasht, IranSaeedKetabchiDepartment of Applied Mathematics, Faculty of Mathematical Sciences University of Guilan, Rasht, IranJournal Article20220615This 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