Tradeoff of Computation Bits and Computing Speed in an Edge Computing System for Sensor Networks

Unmanned aerial vehicle (UAV) enabled mobile-edge computing (MEC) has been recognized as a promising approach for providing enhanced coverage and computation capability to Internet of Things (IoT), especially in the scenario with limited or without infrastructure. In this paper, we consider the UAV assisted partial computation offloading mode MEC system, where ground sensor users are served by a moving UAV equipped with computing server. Computation bits (CB) and computation efficiency (CE) are two vital metrics describe the computation performance of system. To reveal the CB-CE tradeoff, an optimization problem is formulated to maximize the weighted sum of the above two metrics, by optimizing the UAV trajectory jointly with communication resource, as well as the computation resource. As the formulated problem is non-convex, it is difficult to be optimally solved in general. To tackle this issue, we decouple it into two sub-problems: UAV trajectory optimization and resource allocation optimization. We propose an iterative algorithm to solve the two sub-problems by Dinkelbach’s method, Lagrange duality and successive convex approximation technique. Extensive simulation results demonstrate that our proposed resource allocation optimization scheme can achieve better computational performance than the other schemes. Moreover, the proposed alternative algorithm can converge with a few iterations.

Portfolio Optimization with Asset-Liability Ratio Regulation Constraints

This paper considers both a top regulation bound and a bottom regulation bound imposed on the asset-liability ratio at the regulatory time T to reduce risks of abnormal high-speed growth of asset price within a short period of time (or high investment leverage), and to mitigate risks of low assets’ return (or a sharp fall). Applying the stochastic optimal control technique, a Hamilton–Jacobi–Bellman (HJB) equation is derived. Then, the effective investment strategy and the minimum variance are obtained explicitly by using the Lagrange duality method. Moreover, some numerical examples are provided to verify the effectiveness of our results.

Strong Lagrange duality and the maximum principle for nonlinear discrete time optimal control problems

We examine discrete-time optimal control problems with general, possibly non-linear or non-smooth dynamic equations, and state-control inequality and equality constraints. A new generalized convexity condition for the dynamics and constraints is defined, and it is proved that this property, together with a constraint qualification constitute sufficient conditions for the strong Lagrange duality result and saddle-point optimality conditions for the problem. The discrete maximum principle of Pontryagin is obtained in a straightforward manner from the strong Lagrange duality theorem, first in a new form in which the Lagrangian is minimized both with respect to the state and to the control variables. Assuming differentiability, the maximum principle is obtained in the usual form. It is shown that dynamic systems satisfying a global controllability condition with convex costs, have the required convexity property. This controllability condition is a natural extension of the customary directional convexity condition applied in the derivation of the discrete maximum principle for local optima in the literature.