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There are few methods for solving H-weighted nearest correlation matrix (HNCM) problem in the literatures. The main reason is that it is difficult to obtain a computable formula for the projection of a matrix onto the positive semidefinite matrix cone under the H-weight. The alternating direction method (ADM)is applied for solving HNCM problems. At each iteration, a quadratic program with closed-form solution and a projection on positive semidefinite matrix cone without weight are calculated. The method is very simple and easy to be implemented. To speed up the calculation, a modified ADM is also studied. The numerical results show that compared with the existing methods ADM is very efficient for solving HNCM problem. [ABSTRACT FROM AUTHOR]

Levenberg-Marquardt (LM) method is a classical and very efficient method for solving nonlinear equations. However, most of the references on LM method considered the smooth equations. Based on this observation, it is interesting to study the LM method for semismooth equations. A parameter-adjusting LM method for semismooth equations (S-PALM)is constructed to solve semismooth nonlinear equations, in which the parameter is updated based on the ratio between actual reduction and predicted reduction. Under level bounded condition, the global convergence of S-PALM is proved. Under strong BD regularity assumption, the local superlinear convergence rate of S-PALM is established. [ABSTRACT FROM AUTHOR]