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 dual averaging algorithm for multi-agent optimization with coupled constraints
This paper investigates a distributed algorithm for the multi-agent constrained optimization problem, which is to minimize a global objective function formed by a sum of local convex (possibly nonsmooth) functions under both coupled inequality and affine equality constraints. By introducing auxiliary variables, we decouple the constraints and transform the multi-agent optimization problem into a variational inequality problem with a set-valued monotone mapping. We propose a distributed dual averaging...
Distributed Nash equilibrium tracking via the alternating direction method of multipliers
Nash equilibrium is recognized as an important solution concept in non-cooperative game theory due to its broad applicability to economics, social sciences, computer science, and engineering. In view of its importance, substantial progress has been made to seek a static Nash equilibrium using distributed methods. However, these approaches are inapplicable in dynamic environments because, in this setting, the Nash equilibrium constantly changes over time. In this paper, we propose a dynamic algorithm...
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...
Existence of minimizers and necessary conditions in set-valued optimization with equilibrium constraints
In this paper we study set-valued optimization problems with equilibrium constraints (SOPECs) described by parametric generalized equations in the form where both and are set-valued mappings between infinite-dimensional spaces. Such models particularly arise from certain optimization-related problems governed by set-valued variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish general results on the existence of optimal solutions under...
Existence results for quasi variational inequalities.
Existence theorems for the implicit complementarity problem.
Extensão do método de Lemke para a resolução do problema linear complementar com limites superiores
Farkas' lemma of alternative
First- and second-order optimality conditions for mathematical programs with vanishing constraints
We consider a special class of optimization problems that we call Mathematical Programs with Vanishing Constraints, MPVC for short, which serves as a unified framework for several applications in structural and topology optimization. Since an MPVC most often violates stronger standard constraint qualification, first-order necessary optimality conditions, weaker than the standard KKT-conditions, were recently investigated in depth. This paper enlarges the set of optimality criteria by stating first-order...
Forward-backward resolvent splitting methods for general mixed variational inequalities.
General algorithm and sensitivity analysis for variational inequalities.
Generalized co-complementarity problems in -uniformly smooth Banach spaces.
Generalized nonlinear implicit quasivariational inclusions.
Generalized nonlinear variational inequality problems involving multivalued mappings.
Generalized strongly set-valued nonlinear complementarity problems.
Generalized vector complementarity problems with moving cones.
Generic well-posedness for a class of equilibrium problems.