We investigate competitive online algorithms for online convex optimization (OCO) problems with linear in-stage costs, switching costs and ramp constraints. While OCO problems have been extensively studied in the literature, there are limited results on the corresponding online solutions that can attain small competitive ratios. We first develop a powerful computational framework that can compute an optimized competitive ratio based on the class of affine policies. Our computational framework can handle a fairly general class of costs and constraints. Compared with other competitive results in the literature, a key feature of our proposed approach is that it can handle scenarios where infeasibility may arise due to hard feasibility constraints. Second, we design a robustification procedure to produce an online algorithm that can attain good performance for both average-case and worst-case inputs. We conduct a case study on Network Functions Virtualization (NFV) orchestration and scaling to demonstrate the effectiveness of our proposed methods.

中文翻译：

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具有转换成本和斜坡约束的竞争性在线凸优化

我们研究具有线性阶段成本，切换成本和斜坡约束的在线凸优化（OCO）问题的竞争性在线算法。尽管OCO问题已在文献中进行了广泛研究，但在相应的在线解决方案上却可获得有限的竞争结果，因此结果有限。我们首先开发了一个强大的计算框架，该框架可以根据仿射策略类别计算出优化的竞争比率。我们的计算框架可以处理相当普通的成本和约束类。与文献中的其他竞争结果相比，我们提出的方法的主要特征是它可以处理由于严格的可行性约束而可能导致不可行的情况。第二，我们设计了一种鲁棒性程序来生成一种在线算法，该算法对于平均情况和最坏情况的输入都可以达到良好的性能。我们进行了有关网络功能虚拟化（NFV）编排和扩展的案例研究，以证明我们提出的方法的有效性。