A Subspace Method for solving Unconstrained Optimization Problems Without Derivatives

In this paper, we propose a subspace method for solving unconstrained optimization problems without derivatives. In each iteration, we construct a subspace, which enables a large-scale unconstrained optimization problem to be transformed into a lower dimensional subproblem. This paper describes how to use polynomial interpolation model to capture the information of function and its derivatives, and introduces two kinds of subspace algorithms of different dimensions without derivatives. The new algorithm not only has less computational complexity, but also can be applied to the problem that the derivative information is difficult to obtain or even can not be completely solved.