This technical note considers a distributed convex optimization problem with nonsmooth cost functions and coupled nonlinear inequality constraints. To solve the problem, we first propose a modified Lagrangian function containing local multipliers and a nonsmooth penalty function. Then we construct a distributed continuous-time algorithm by virtue of a projected primal-dual subgradient dynamics. Based on the nonsmooth analysis and Lyapunov function, we obtain the existence of the solution to the nonsmooth algorithm and its convergence.

This paper develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. We then analyze critical values for parameters in the proposed method and prove that the rate of convergence is $O(\frac{1}{t^2})$ with properly chosen parameters. As far as we know, this is the first continuous-time primal-dual accelerated method that can obtain the optimal rate. In addition, we apply the proposed method to two network optimization problems, a distributed optimization problem with consensus constraints and a distributed extended monotropic optimization problem, and obtain two variant distributed algorithms. Finally, numerical simulations are given to demonstrate the efficacy of the proposed method.

This paper focuses on a distributed convex optimization problem with set constraints, where the local objective functions are convex but not necessarily differentiable. We employ an exact penalty method for the constrained optimization problem to avoid the projection of subgradients to convex sets, which may result in problems about algorithm trajectories caused by maybe non-convex differential inclusions and quite high computational cost. To effectively find a suitable gain of the penalty function online, we propose an adaptive distributed algorithm with help of the adaptive control idea in order to achieve an exact solution without any priori computation or knowledge of the objective functions. By virtue of convex and non-smooth analysis, we give a rigorous proof for the convergence of the proposed continuoustime algorithm.

Lane change is a common-yet-challenging driving behavior for automated vehicles. To improve the safety and efficiency of automated vehicles, researchers have proposed various lane-change decision models. However, most of the existing models consider lane-change behavior as a one-player decision-making problem, ignoring the essential multi-agent properties when vehicles are driving in traffic. Such models lead to deficiencies in interaction and collaboration between vehicles, which results in hazardous driving behaviors and overall traffic inefficiency. In this paper, we revisit the lane-change problem and propose a bi-level lane-change behavior planning strategy, where the upper level is a novel multi-agent deep reinforcement learning (DRL) based lane-change decision model and the lower level is a negotiation based right-of-way assignment model. We promote the collaboration performance of the upper-level lane-change decision model from three crucial aspects. First, we formulate the lane-change decision problem with a novel multi-agent reinforcement learning model, which provides a more appropriate paradigm for collaboration than the single-agent model. Second, we encode the driving intentions of surrounding vehicles into the observation space, which can empower multiple vehicles to implicitly negotiate the right-of-way in decision-making and enable the model to determine the right-of-way in a collaborative manner. Third, an ingenious reward function is designed to allow the vehicles to consider not only ego benefits but also the impact of changing lanes on traffic, which will guide the multi-agent system to learn excellent coordination performance. With the upper-level lane-change decisions, the lower-level right-of-way assignment model is used to guarantee the safety of lane-change behaviors. The experiments show that the proposed approaches can lead to safe, efficient, and harmonious lane-change behaviors, which boosts the collaboration between vehicles and in turn improves the safety and efficiency of the overall traffic. Moreover, the proposed approaches promote the microscopic synchronization of vehicles, which can lead to the macroscopic synchronization of traffic flow.

In this note, we investigate a continuous-time distributed optimization problem with time-varying cost functions and affine formation constraints, which are described by the stress matrices rather than the standard Laplacians. The objective is to minimize the sum of local time-varying cost functions, each of which is known by only one individual agent. The optimal solution is a time-varying affine transformation of a nominal configuration rather than some constants. To tackle the difficulty caused by the dynamic aspect of the local cost functions and handle affine formation constraints, the fixed-time distributed estimator and distributed gradient tracking technique are developed respectively to compensate the time variation of solution trajectory and calculate the weighted sum of local gradients to eliminate the tracking error. The time-varying optimal solution trajectory is thus accurately tracked with the proposed estimator-based gradient tracking algorithm. Using appropriately chosen coefficients, the tracking error is guaranteed to vanish at an exponential rate. The proposed estimator-based gradient tracking algorithm is further validated through numerical simulations.