In this paper, zero duality gap conditions in nonconvex optimization are investigated. It is considered that dual problems can be constructed with respect to the weak conjugate functions, and/or directly by using an augmented Lagrangian formulation. Both of these approaches and the related strong duality theorems are studied and compared in this paper. By using the weak conjugate functions approach, special cases related to the optimization problems with equality and inequality constraints are studied and the zero duality gap conditions in terms of objective and constraint functions, are established. Illustrative examples are provided.

中文翻译：

---

关于非凸优化中的弱共轭，增强拉格朗日数和对偶性

本文研究了非凸优化中的零对偶间隙条件。可以考虑针对弱共轭函数构造对偶问题，和/或直接使用增强的拉格朗日公式来构造对偶问题。本文对这两种方法以及相关的强对偶定理进行了研究和比较。通过使用弱共轭函数方法，研究了具有等式和不等式约束的优化问题的特殊情况，并建立了基于目标和约束函数的零对偶间隙条件。提供了说明性示例。