Approximations to the Clarke Generalized Jacobians and Nonsmooth Least-Squares Minimization

摘要: Here we use a uniform approximation to the Clarke generalized Jacobian design an algorithm for solving class of nonsmooth least-squares minimization problems: \(\min \phi (x) \equiv \frac{1}{2}\sum\nolimits_{i = 1}^m {{f_i}{{(x)}^2} \frac{1}{2}F{{(x)}^T}F(x),} \) where F : ℝ n → m is locally Lipschitz mapping. We approximate subdifferential φ by approximating F. Regularity conditions global convergence are discussed in details.