Edge computing has become a new paradigm in response to the increasing demand for time-sensitive and computation-intensive tasks, offering advantages over traditional cloud computing due to its proximity to terminal devices and low transmission latency. Container-based edge computing provides a powerful way to deploy applications and manage resources at the edge of the network. However, optimizing the caching strategy is crucial due to the limited capacity of the edge server, and the startup time of services on edge servers is a crucial consideration when making decisions regarding computation offloading and service caching. In this paper, taking into account container startup time, we formulate an optimization model for the task offloading, container caching, and image caching in the container-based edge computing architectures, which is a nonlinear integer programming (NLIP) problem that is NP-hard. We then propose an algorithm that finds the global optimal solution to this NLIP problem by transforming it into an equivalent linear integer programming problem. Our simulation experiments demonstrate that our proposed algorithm can effectively and fast find a globally optimal solution to the underlying problem and that our model outperforms the existing model without considering the container start-up time.

In this paper, we consider the so-called worst-case linear optimization (WCLO) with uncertainties on the right-hand side of the constraints. Such a problem often arises in applications such as in systemic risk estimation in finance and stochastic optimization. We first show that the WCLO problem with the uncertainty set corresponding to the [Formula: see text]p-norm ((WCLOp)) is NP-hard for p ɛ (1,∞). Second, we combine several simple optimization techniques, such as the successive convex optimization method, quadratic convex relaxation, initialization, and branch-and-bound (B&B), to develop an algorithm for (WCLO2) that can find a globally optimal solution to (WCLO2) within a prespecified ε-tolerance. We establish the global convergence of the algorithm and estimate its complexity. We also develop a finite B&B algorithm for (WCLO∞) to identify a global optimal solution to the underlying problem, and establish the finite convergence of the algorithm. Numerical experiments are reported to illustrate the effectiveness of our proposed algorithms in finding globally optimal solutions to medium and large-scale WCLO instances.