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In this paper, a new alternating direction trust region method based on conicmodel is used to solve unconstrained optimization problems. By use of thealternating direction method, the new conic model trust region subproblem issolved by two steps in two orthogonal directions. This new idea overcomes theshortcomings of conic model subproblem which is difficult to solve. Then theglobal convergence of the method under some reasonable conditions isestablished. Numerical experiment shows that this method may be better than thedogleg method to solve the subproblem, especially for large-scale problems.

A new alternating direction trust region method based on conic model for solving unconstrained optimization