Gurman摄动变换在非凸全局优化中的应用

Non-convex Global Optimization with Gurman Perturbation

讨论球约束下的一类非凸函数的全局优化问题.把全局优化问题转化为奇异最优控制问题,通过Gurman摄动变换引入canonical全局优化方法,得到判别全局优化问题的最优解的等价性条件和必要条件,并证明球约束下非凸二次函数的全局优化问题的最优解的一个充要条件.

The global optimization of a non-convex function over a sphere is investigated by the Gurman perturbation method and the canonical backward flow. The constrained optimization is converted into a singular optimal control problem for solving non-convex global optimization. A sufficient and necessary optimality condition is obtained for the non-convex quadratic optimization over a sphere.