On pseudo gradient search for solving nonlinear multiregression with the Choquet integral

The objective function in some real optimization problems may not be differentiable with respect to the unknown parameters at some points such that the gradient does not exist at those points. Replacing the classical gradient search, the method of pseudo gradient search has been proposed and used for solving nonlinear optimization problems, such as nonlinear multiregression based on the Choquet integral with a linear core. It is a local search with rapid search speed. To improve the search tactics, a random angle search in randomly selected dimensions is also involved. Our experiments show that the proposed pseudo gradient search is effective and efficient. It can be widely used for solving nonlinear optimization problems with continuous objective function.