Applications of the proximal difference-of-convex algorithm with extrapolation in optimal correction

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.

Keywords:

Proximal difference-of-convex , extrapolation , classical obstacle problem , equilibrium problems , linear inequalities , nonconvex , level-bounded