On the choice of parameters for the weighting method in vector optimization

• 成果类型: Article; Proceedings Paper
• 署名作者: Drummond, L. M. Grana; Maculan, N.; Svaiter, B. F.
• 署名单位: Universidade Federal do Rio de Janeiro; Universidade Federal do Rio de Janeiro
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-006-0071-7
• 发表日期: 2008
• 页码: 201-216
• 关键词: scalarization

摘要

We present a geometrical interpretation of the weighting method for constrained (finite dimensional) vector optimization. This approach is based on rigid movements which separate the image set from the negative of the ordering cone. We study conditions on the existence of such translations in terms of the boundedness of the scalar problems produced by the weighting method. Finally, using recession cones, we obtain the main result of our work: a sufficient condition under which weighting vectors yield solvable scalar problems.