AN INEXACT PROXIMAL DC ALGORITHM FOR THE LARGE-SCALE CARDINALITY CONSTRAINED MEAN-VARIANCE MODEL IN SPARSE PORTFOLIO SELECTION

Optimization problem of cardinality constrained mean-variance(CCMV)model for sparse portfolio selection is considered.To overcome the difficulties caused by cardinality constraint,an exact penalty approach is employed,then CCMV problem is transferred into a difference-of-convex-functions(DC)problem.By exploiting the DC structure of the gained problem and the superlinear convergence of semismooth Newton(ssN)method,an inexact proximal DC algorithm with sieving strategy based on a majorized ssN method(siPDCA-mssN)is proposed.For solving the inner problems of siPDCA-mssN from dual,the second-order information is wisely incorporated and an efficient mssN method is employed.The global convergence of the sequence generated by siPDCA-mssN is proved.To solve large-scale CCMV problem,a decomposed siPDCA-mssN(DsiPDCA-mssN)is introduced.To demonstrate the efficiency of proposed algorithms,siPDCA-mssN and DsiPDCA-mssN are compared with the penalty proximal alternating linearized minimization method and the CPLEX(12.9)solver by performing numerical experiments on realword market data and large-scale simulated data.The numerical results demonstrate that siPDCA-mssN and DsiPDCA-mssN outperform the other methods from computation time and optimal value.The out-of-sample experiments results display that the solutions of CCMV model are better than those of other portfolio selection models in terms of Sharp ratio and sparsity.