Abstract: The Hessian matrix in a quadratic model was approximated by a Hessian matrix satisfying the modified secant equation, and the search direction was derived by minimizing the quadratic model in a threedimensional subspace. Combined with some nonmonotonic line search strategies and restart techniques, we proposed an improved threedimensional subspace minimization conjugate gradient algorithm. Under some reasonable assumptions, the global convergence of the algorithm was proved. For the test function set named Andrei, numerical experiment verified the effectiveness of the new algorithm.

Key words: largescale unconstrained optimization, conjugate gradient method, modified secant equation, Wolfe line search, global convergence