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.
翻译:在本文中,我们有兴趣根据对有效解决对称电子价值互补问题(SEICP)和对称电子价值互补问题(SQECP)的精确线搜索,制定加速的Conferation(DC)编程算法。我们首先证明,任何SeiCP都相当于SECP, 仅具有对称正确定矩阵。然后,我们为SEICP的两种等同配方(即对数配方和四方配方)建立了DC编程配方(即对数配方和四方配方),并提议加速DC算法(BDCA),将经典DCA与价格低廉的精确行程搜索相结合,找出加速的二元性问题的真正根源。我们展示了SQEICP和SEICP之间的等同性,并将BDCA扩大到SQECP。 拟议的BDCA和DCA对KITRO的两种等价配方配方配方配方(即对配方配方配方和四方配方配方配方),并提议加速的DC的加速算法(BDCA),将经典的CA和SQECP与成本精确搜索搜索搜索,通过合成数据定法,特别是卡加速的合成和卡内市级拼法。