Description of all solutions of a linear complementarity problem.
Distributed aggregative optimization with quantized communication
In this paper, we focus on an aggregative optimization problem under the communication bottleneck. The aggregative optimization is to minimize the sum of local cost functions. Each cost function depends on not only local state variables but also the sum of functions of global state variables. The goal is to solve the aggregative optimization problem through distributed computation and local efficient communication over a network of agents without a central coordinator. Using the variable tracking...
Distributed optimization for multi-agent system over unbalanced graphs with linear convergence rate
Distributed optimization over unbalanced graphs is an important problem in multi-agent systems. Most of literatures, by introducing some auxiliary variables, utilize the Push-Sum scheme to handle the widespread unbalance graph with row or column stochastic matrix only. But the introduced auxiliary dynamics bring more calculation and communication tasks. In this paper, based on the in-degree and out-degree information of each agent, we propose an innovative distributed optimization algorithm to reduce...
Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities
A dual-weighted residual approach for goal-oriented adaptive finite elements for a class of optimal control problems for elliptic variational inequalities is studied. The development is based on the concept of C-stationarity. The overall error representation depends on primal residuals weighted by approximate dual quantities and vice versa as well as various complementarity mismatch errors. Also, a priori bounds for C-stationary points and associated multipliers are derived. Details on the numerical...