Convergence of derivative-free nonmonotone Direct Search Methods for unconstrained and box-constrained mixed-integer optimization
提出一类非单调直接搜索方法，用于求解无约束和箱约束混合整数优化问题，引入准下降方向概念，无需导数计算，初步数值实验效果良好。
Abstract This paper presents a class of nonmonotone Direct Search Methods that converge to stationary points of unconstrained and boxed constrained mixed-integer optimization problems. A new concept is introduced: the quasi-descent direction. A point x is stationary on a set of search directions if there exists no feasible qdd on that set. The method does not require the computation of derivatives nor the explicit manipulation of asymptotically dense matrices. Preliminary numerical experiments carried out on small to medium problems are encouraging.