Many engineering and scientific applications, e.g. resource allocation, control of hybrid systems, scheduling, etc., require the solution of mixed-integer non-linear problems (MINLPs). Problems of such class combine the high computational burden arising from considering discrete variables with the complexity of non-linear functions. As a consequence, the development of algorithms able to efficiently solve medium-large MINLPs is still an interesting field of research. In the last decades, several approaches to tackle MINLPs have been developed. Some of such approaches, usually defined as exact methods, aim at finding a globally optimal solution for a given MINLP at expense of a long execution time, while others, generally defined as heuristics, aim at discovering suboptimal feasible solutions in the shortest time possible. Among the various proposed paradigms, outer approximation (OA) and feasibility pump (FP), respectively as exact method and as heuristic, deserve a special mention for the number of relevant publications and successful implementations related to them. In this paper we present a new exact method for convex mixed-integer non-linear programming called proximal outer approximation (POA). POA blends the fundamental ideas behind FP into the general OA scheme that attepts to yield faster and more robust convergence with respect to OA while retaining the good performances in terms of fast generation of feasible solutions of FP.

许多工程和科学应用，例如资源分配，混合系统的控制，调度等，都需要解决混合整数非线性问题（MINLP）。这类问题将考虑离散变量带来的高计算负担与非线性函数的复杂性结合在一起。因此，开发能够有效解决中型MINLP的算法仍然是一个有趣的研究领域。在过去的几十年中，已经开发出几种解决MINLP的方法。这些方法中的一些通常定义为精确方法，旨在以给定的MINLP查找较长时间的执行时间来找到全局最佳解决方案，而其他一些通常定义为启发式方法，旨在在尽可能短的时间内发现次优可行解。在各种提议的范例中，分别作为精确方法和启发式方法的外部近似（OA）和可行性泵（FP），应特别提及相关出版物的数量和与之相关的成功实现。在本文中，我们提出了一种新的精确方法，用于凸混合整数非线性规划，称为近端外部逼近（POA）。POA将FP背后的基本思想融合到了通用OA方案中，该方案试图相对于OA产生更快，更强大的融合，同时在快速生成FP可行解决方案方面保留良好的性能。在本文中，我们提出了一种新的精确方法，用于凸混合整数非线性规划，称为近端外部逼近（POA）。POA将FP背后的基本思想融合到了通用OA方案中，该方案试图相对于OA产生更快，更强大的融合，同时在快速生成FP可行解决方案方面保留良好的性能。在本文中，我们提出了一种新的精确方法，用于凸混合整数非线性规划，称为近端外部逼近（POA）。POA将FP背后的基本思想融合到了通用OA方案中，该方案试图相对于OA产生更快，更强大的融合，同时在快速生成FP可行解决方案方面保持良好的性能。