Global optimization in Hilbert space
提出一种完全搜索算法，用于求解一类非凸、可能无限维的优化问题至全局最优，并给出最坏情况运行时间上界，证明算法在有限时间内收敛到ε-次优全局解。
We propose a complete-search algorithm for solving a class of non-convex, possibly infinite-dimensional, optimization problems to global optimality. We assume that the optimization variables are in a bounded subset of a Hilbert space, and we determine worst-case run-time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set. Because these run-time bounds are independent of the number of optimization variables and, in particular, are valid for optimization problems with infinitely many optimization variables, we prove that the algorithm converges to an $$\varepsilon $$ -suboptimal global solution within finite run-time for any given termination tolerance $$\varepsilon > 0$$ . Finally, we illustrate these results for a problem of calculus of variations.