发表机构
Interdisciplinary Center for Scientific Computing, University of Heidelberg; Institute of Mathematics, Clausthal University of Technology（海德堡大学跨学科计算科学中心; 克劳塔尔工业大学数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对块消失约束数学规划，扩展约束规范理论并证明LICQ型条件蕴含GCQ，提出分段梯度流方法直接计算强稳定点，数值实验验证其鲁棒性。
AI 中文摘要
具有块消失约束的数学规划（MP-BVCs）是一类具有挑战性的优化问题，因为标准约束规范会失效。基于经典MPVC（即块大小为1的MPBVC）的现有理论，我们扩展了MPBVC的约束规范理论，并证明了已知的MPBVC的LICQ型条件蕴含Guignard约束规范（GCQ）。一种新颖的分段梯度流方法在GCQ下收敛。该方法直接计算强稳定点，是经典MPVC问题分段梯度流方法的推广。在多个具有两个甚至三个施加荷载的桁架拓扑设计实例上的数值实验证明了该方法的鲁棒性和有效性。
英文摘要
Mathematical Programs with Blocks of Vanishing Constraints (MP-BVCs) are a challenging class of optimization problems due to the loss of standard constraint qualifications. Based on existing theory for classical MPVCs, i.e., MPBVC with block size one, we extend the constraint qualification theory for MPBVCs and show that the known LICQ-type condition for MPBVCs implies the Guignard Constraint Qualification (GCQ). A novel piecewise gradient flow approach converges under GCQ. It directly computes strongly stationary points and is an extension of the piecewise gradient flow approach for classic MPVC problems. Numerical experiments on several truss topology design instances with two and even three applied load forces demonstrate the robustness and effectiveness of the method.
Comments38 pages
