Convergent upper bounds in global minimization with nonlinear equality constraints

• 成果类型: Article
• 署名作者: Fuellner, Christian; Kirst, Peter; Stein, Oliver
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01493-2
• 发表日期: 2021
• 页码: 617-651
• 关键词: optimization method; alpha-bb; branch; algorithm; PROGRAMS; nlps; EXISTENCE

摘要

We address the problem of determining convergent upper bounds in continuous non-convex global minimization of box-constrained problems with equality constraints. These upper bounds are important for the termination of spatial branch-and-bound algorithms. Our method is based on the theorem of Miranda which helps to ensure the existence of feasible points in certain boxes. Then, the computation of upper bounds at the objective function over those boxes yields an upper bound for the globally minimal value. A proof of convergence is given under mild assumptions. An extension of our approach to problems including inequality constraints is possible.