Variable metric proximal stochastic variance reduced gradient methods for nonconvex nonsmooth optimization

<p style='text-indent:20px;'>We study the problem of minimizing sum two functions. The first function is average a large number nonconvex component functions and second convex (possibly nonsmooth) that admits simple proximal mapping. With diagonal Barzilai-Borwein stepsize for updating metric, we propose variable metric stochastic variance reduced gradient method in mini-batch setting, named VM-SVRG. It proved VM-SVRG converges sublinearly to stationary point expectation. We further suggest variant achieve linear convergence rate expectation problems satisfying Polyak-Łojasiewicz inequality. complexity lower than method, same as method. Numerical experiments are conducted on standard data sets. Comparisons with other advanced methods show efficiency proposed method.</p>