An Inexact Proximal DC Algorithm for the Large-Scale Cardinality Constrained Mean-Variance Model in Sparse Portfolio Selection (Journal of Computational Mathematics, 2024)
Optimization problem of cardinality constrained mean-variance (CCMV) model forsparse portfolio selection is considered. To overcome the difficulties caused by cardinalityconstraint, an exact penalty approach is employed, then CCMV problem is transferredinto a difference-of-convex-functions (DC) problem. By exploiting the DC structure of thegained problem and the superlinear convergence of semismooth Newton (ssN) method, aninexact 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) isintroduced. To demonstrate the efficiency of proposed algorithms, siPDCA-mssN andDsiPDCA-mssN are compared with the penalty proximal alternating linearized minimization method and the CPLEX(12.9) solver by performing numerical experiments on real-word market data and large-scale simulated data. The numerical results demonstratethat siPDCA-mssN and DsiPDCA-mssN outperform the other methods from computationtime and optimal value. The out-of-sample experiments results display that the solutionsof CCMV model are better than those of other portfolio selection models in terms of Sharpratio and sparsity.
Keywords: Sparse portfolio selection; Cardinality constrained mean-variance model; Inexact proximal difference-of-convex-functions algorithm; Sieving strategy; Decomposed strategy.