In this chapter, we present several optimization algorithms that utilize complementarity functions. As discussed in Chap.  2 , there are four well-established approaches for solving the NCP, each of which can be extended to broader settings such as the SOCCP, the SDCP, and the SCCP. Accordingly, the chapter is organized into four sections, with each section illustrating one or two representative algorithms within a given approach, accompanied by various complementarity functions to highlight the algorithmic applications of C-functions. Numerous related algorithms employing C-functions can also be found in the literature; for further reference, see  [1–9].