Algorithms for problem decomposition and splitting in optimization and the solving of variational inequalities have largely depended on assumptions of convexity or monotonicity. Here, a way of “eliciting” convexity or monotonicity is developed which can get around that limitation. It supports a procedure called the progressive decoupling algorithm, which is derived from the proximal point algorithm through passing to a partial inverse, localizing and rescaling. In the optimization setting, elicitability of convexity corresponds to a new and very general kind of second-order sufficient condition for a local minimum. Applications are thereby opened up to problem decomposition and splitting even in nonconvex optimization, moreover with augmented Lagrangians for subproblems assisting in the implementation.

中文翻译：

---

具有可凸的凸性或单调性的优化和变分不等式中链的渐进解耦

优化中的问题分解和分裂算法以及变分不等式的求解很大程度上取决于凸性或单调性的假设。在这里，开发了一种“引发”凸度或单调性的方法，可以克服该限制。它支持一种称为渐进去耦算法的过程，该过程是通过传递给局部逆，局部化和重新缩放而从近端点算法得出的。在优化设置中，凸的可引出性对应于一种新的且非常通用的二阶充分条件，用于局部最小值。因此，即使在非凸优化中，应用程序也可以进行问题分解和分解，此外，还有用于子问题的扩展拉格朗日函数有助于实现。