A limited memory q-BFGS (Broyden–Fletcher–Goldfarb–Shanno) method is presented for solving unconstrained optimization problems. It is derived from a modified BFGS-type update using q-derivative (quantum derivative). The use of Jackson’s derivative is an effective mechanism for escaping from local minima. The q-gradient method is complemented to generate the parameter q for computing the step length in such a way that the search process gradually shifts from global in the beginning to almost local search in the end. Further, the global convergence is established under Armijo-Wolfe conditions even if the objective function is not convex. The numerical experiments show that proposed method is potentially efficient.

提出了有限内存q -BFGS（Broyden-Fletcher-Goldfarb-Shanno）方法，用于解决无约束的优化问题。它是使用q导数（量子导数）从修改后的BFGS类型更新得出的。使用杰克逊导数是逃避局部极小值的有效机制。该q -gradient方法进行补充，以生成所述参数 q用于计算以这样的方式，步长，搜索过程从全球逐渐转变在开始到底几乎局部搜索。此外，即使目标函数不是凸的，在Armijo-Wolfe条件下也会建立全局收敛。数值实验表明，该方法是有效的。