Abstract
In work of Roman A. Polyak [R.A. Polyak, Math. Program. 92 (2002) 197–235.], the Modified Chen-Harker-Kanzow-Smale (CHKS) function was studied to relate a multiplier method and an Interior Prox method with the second order distance function. Independently, the dislocated hyperbolic penalty function (DHPF) was proposed by A.E. Xavier (1992). DHPF was rewritten and studied in [L. Mallma Ramirez, N. Maculan, A.E. Xavier and V.L. Xavier, RAIRO:RO 57 (2023) 2941–2950.] and [L. Mallma Ramirez, N. Maculan, A.E. Xavier and V.L. Xavier, J. Convex Anal. To appear (2024).]. Thus, this function was called the dislocated hyperbolic function (DHF). In this work, we note that DHF is a particular case of CHKS function. Then we will call the DHF function as the dislocation hyperbolic transformation function.