A globally convergent proximal Newton-type method in nonsmooth convex optimization

The paper proposes and justifies a new algorithm of the proximal Newton type to solve broad class nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions techniques variational analysis, we establish implementable results global convergence proposed as well its local with superlinear quadratic rates. For certain structured problems, obtained conditions do not require Lipschitz continuity corresponding Hessian mappings that is crucial assumption used in literature ensure other algorithms type. conducted numerical experiments solving \(l_1\) regularized logistic regression model illustrate possibility applying deal practically important problems.