A variable metric and nesterov extrapolated proximal DCA with backtracking for a composite DC program

In this paper, we consider a composite difference-of-convex (DC) program, whose objective function is the sum of smooth convex with Lipschitz continuous gradient, proper closed and function, concave function. This problem has many applications in machine learning data science. The proximal DCA (pDCA), special case classical algorithm (DCA), as well two Nesterov-type extrapolated – ADCA (Phan et al. IJCAI:1369–1375, 2018) pDCAe (Wen Comput. Optim. Appl. 69:297–324, can solve problem. algorithmic stepsizes pDCA, pDCAe, are fixed determined by estimating prior smoothness parameter loss However, such an estimate may be hard to obtain or poor some real-world applications. Motivated difficulty, propose variable metric Nesterov backtracking (SPDCAe), which combines line search procedure (not necessarily monotone) Nesterov's extrapolation for potential acceleration; moreover, method incorporated better local approximation. Numerical simulations on sparse binary logistic regression compressed sensing Poisson noise demonstrate effectiveness our proposed method.