无穷维空间中新Farkas型结果

Farkas-type Results with Conjugate Functions in Infinite-dimensional Setting

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.