摘要
R.I.Bot和G.Wanka(SIAM J Optim,2005,15(2):540-554.)利用凸优化问题中的共轭对偶定理,研究了两类对偶问题,即广义Fenchel对偶问题和Fenchel-Lagrange对偶问题,提出了有限维空间中具有有限个和无限个凸限制的不等式系统的新Farkas型结果.在无穷维空间中推广了他们的结论,得到无穷维空间中有限个和无限个凸限制的不等式系统的新Farkas型结果.
R. I. Bot and G. Wanka( SIAM J Optim,2005,15(2) :540-554. ) studied two kinds of dual problem, namely, an extended Fenchel type and Fenchel-Lagrange dual based on the conjugate theorem in convex optimization problem. They presented some new Farkas-type results for inequality systems involving a finite as well as an infinite number of convex constraints in finite-dimensional spaces. Inspired and motivated by the research works above, we provide the Farkas-type results in infinite-dimensional setting.
出处
《四川师范大学学报(自然科学版)》
CAS
CSCD
北大核心
2008年第3期311-315,共5页
Journal of Sichuan Normal University(Natural Science)
基金
四川省青年科技基金(06ZQ026-013)资助项目