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This paper addresses the study of a new class of nonsmooth optimizationproblems, where the objective is represented as a difference of two generallynonconvex functions. We propose and develop a novel Newton-type algorithm tosolving such problems, which is based on the coderivative generatedsecond-order subdifferential (generalized Hessian) and employs advanced toolsof variational analysis. Well-posedness properties of the proposed algorithmare derived under fairly general requirements, while constructive convergencerates are established by using additional assumptions including theKurdyka--{\L}ojasiewicz condition. We provide applications of the mainalgorithm to solving a general class of nonsmooth nonconvex problems ofstructured optimization that encompasses, in particular, optimization problemswith explicit constraints. Finally, applications and numerical experiments aregiven for solving practical problems that arise in biochemical models,constrained quadratic programming, etc., where advantages of our algorithms aredemonstrated in comparison with some known techniques and results.

Coderivative-Based Semi-Newton Method in Nonsmooth Difference Programming