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Distributed aggregative optimization with quantized communication

Ziqin Chen, Shu Liang (2022)

Kybernetika

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

Songsong Cheng, Shu Liang (2020)

Kybernetika

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

M. Hintermüller, R. H. W. Hoppe, C. Löbhard (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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

Truong Q. Bao, Boris S. Mordukhovich (2007)

Applications of Mathematics

In this paper we study set-valued optimization problems with equilibrium constraints (SOPECs) described by parametric generalized equations in the form 0 ∈ G ( x ) + Q ( x ) , where both G and Q 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...

First- and second-order optimality conditions for mathematical programs with vanishing constraints

Tim Hoheisel, Christian Kanzow (2007)

Applications of Mathematics

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...

Global convergence property of modified Levenberg-Marquardt methods for nonsmooth equations

Shou-qiang Du, Yan Gao (2011)

Applications of Mathematics

In this paper, we discuss the globalization of some kind of modified Levenberg-Marquardt methods for nonsmooth equations and their applications to nonlinear complementarity problems. In these modified Levenberg-Marquardt methods, only an approximate solution of a linear system at each iteration is required. Under some mild assumptions, the global convergence is shown. Finally, numerical results show that the present methods are promising.

Inexact Newton-type method for solving large-scale absolute value equation A x - | x | = b

Jingyong Tang (2024)

Applications of Mathematics

Newton-type methods have been successfully applied to solve the absolute value equation A x - | x | = b (denoted by AVE). This class of methods usually solves a system of linear equations exactly in each iteration. However, for large-scale AVEs, solving the corresponding system exactly may be expensive. In this paper, we propose an inexact Newton-type method for solving the AVE. In each iteration, the proposed method solves the corresponding system only approximately. Moreover, it adopts a new line search technique,...

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