We propose a first-order method to solve the cubic regularization subproblem (CRS) based on novel reformulation. The reformulation is constrained convex optimization problem whose feasible region admits an easily computable projection. Our requires computing minimum eigenvalue of Hessian. To avoid expensive computation exact eigenvalue, we develop surrogate where replaced with approximate one. ...

In recent years, machine component design has been a major concern for researchers. Emphasis placed especially on the analysis of bearing systems in order to avoid detrimental contact. The shaft misalignment is one most problems that affects directly operating conditions these components. this context, present study proposes reduced-order method "Proper Generalized Decomposition" (PGD) using se...