ABSTRACT

We present new results on optimization problems where the involved functions are evenly convex. By means of a generalized conjugation scheme and the perturbation theory introduced by Rockafellar, we propose an alternative dual problem for a general optimization one defined on a separated locally convex topological space. Sufficient conditions for converse and total duality involving the even convexity of the perturbation function and c-subdifferentials are given. Formulae for the c-subdifferential and biconjugate of the objective function of a general optimization problem are provided, too. We also characterize the total duality by means of the saddle-point theory for a notion of Lagrangian adapted to the considered framework.

摘要

我们提出了有关优化问题的新结果，其中所涉及的函数是均匀凸的。通过广义共轭方案和 Rockafellar 引入的微扰理论，我们提出了一个替代对偶问题，用于定义在分离的局部凸拓扑空间上的一般优化问题。给出了包含微扰函数的偶凸性和c 次微分的逆对偶和全对偶的充分条件。还提供了一般优化问题的目标函数的c 次微分和双共轭的公式。我们还通过适用于所考虑框架的拉格朗日概念的鞍点理论来表征总对偶性。