We establish a general duality theorem in a generalized conjugacy framework, which generalizes a classical result on the minimization of a convex function over a closed convex cone. Our theorem yields two quasiconvex duality schemes; one of them is of the surrogate duality type and is applicable to problems having an evenly quasiconvex objective function, whereas the other one is applicable to problems with Lipschitz quasiconvex objective functions and yields duals whose objective functions do not involve any surrogate constraint.

中文翻译：

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闭凸锥上拟凸面最小化的对偶性

我们在广义共轭框架中建立了一般对偶定理，该定理概括了在封闭凸锥上最小化凸函数的经典结果。我们的定理产生了两个拟凸对偶方案；其中一种是代理对偶类型，适用于具有均匀拟凸目标函数的问题，而另一种适用于具有 Lipschitz 拟凸目标函数的问题，并产生目标函数不涉及任何代理约束的对偶。