On the use of finite differences in the multistart method for solving a certain class of global optimization (Q1965357)

A global optimization problem \[ F(x) \to{min}\atop{x\in{\mathbb R}_{k}} \eqno (1) \] where \({\mathbb R}_{k}\) is a \(k\)-dimensional Euclidean space, \(F(x)\) is a multi-extremal and parametric regular function is considered. As a rule some gradient methods are additionally used to solve the problem (1) by a multi-start method. An extension of the multi-start method is proposed to solve the problem (1) when the function \(F(x)\) has a special \(\gamma\)-regular structure.