AbstractThis paper presents a new parallel conjugate direction method for unconstrained, n-dimensional minimization problems. Starting from one point, the method performs n line searches concurrently along n conjugate directions of the approximate Hessian to derive a new point and generate n new conjugate directions. For deriving the new point, a linear formula is presented, and its convergence properties are discussed. The n new conjugate directions are generated mostly in parallel without explicitly using the approximate Hessian. For quadratic problems, it is shown that the method converges in two parallel iterations. For nonquadratic problems, safeguard steps are taken to guarantee monotonic decency and global convergence. A sufficient condition for“rapid”convergence is also presented. Numerical testing results indicate that, comparing with the conventional conjugate gradient method, the parallel method takes less (parallel) iterations and less function evaluations for all test problems, lmd is most effective for problems whose Hessians change little from iteration to iteration.