  In this paper, we are interested in developing an accelerated
Difference-of-Convex (DC) programming algorithm based on the exact line search
for efficiently solving the Symmetric Eigenvalue Complementarity Problem
(SEiCP) and Symmetric Quadratic Eigenvalue Complementarity Problem (SQEiCP). We
first proved that any SEiCP is equivalent to SEiCP with symmetric positive
definite matrices only. Then, we established DC programming formulations for
two equivalent formulations of SEiCP (namely, the logarithmic formulation and
the quadratic formulation), and proposed the accelerated DC algorithm (BDCA) by
combining the classical DCA with inexpensive exact line search by finding real
roots of a binomial for acceleration. We demonstrated the equivalence between
SQEiCP and SEiCP, and extended BDCA to SQEiCP. Numerical simulations of the
proposed BDCA and DCA against KNITRO, FILTERED and MATLAB FMINCON for SEiCP and
SQEiCP on both synthetic datasets and Matrix Market NEP Repository are
reported. BDCA demonstrated dramatic acceleration to the convergence of DCA to
get better numerical solutions, and outperformed KNITRO, FILTERED, and FMINCON
solvers in terms of the average CPU time and average solution precision,
especially for large-scale cases.
