A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions

作     者：Fowkes, Jaroslav M. Gould, Nicholas I. M. Farmer, Chris L. 

作者机构：Univ Edinburgh Sch Math Edinburgh EH9 3JZ Midlothian Scotland Rutherford Appleton Lab Computat Sci & Engn Dept Chilton OX11 0QX Oxon England Univ Oxford Math Inst Oxford OX1 3LB England 

出 版 物：《JOURNAL OF GLOBAL OPTIMIZATION》 (全局最优化杂志)

年 卷 期：2013年第56卷第4期

页      面：1791-1815页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：EPSRC [EP/F005369/1  EP/E053351/1  EP/I013067/1] Funding Source: UKRI 

主　　题：Global optimization Lipschitzian optimization Branch and bound Nonconvex programming 

摘      要：We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation techniques to the objective function within an overlapping branch and bound algorithm for convex constrained global optimization. Unlike other branch and bound algorithms, lower bounds are obtained via nonconvex underestimators of the function. For a numerical example, we apply the proposed branch and bound algorithm to radial basis function approximations.