Distributed dual averaging algorithm for multi-agent optimization with coupled constraints

Zhipeng Tu; Shu Liang

Displaying similar documents to “Distributed dual averaging algorithm for multi-agent optimization with coupled constraints”

New hybrid conjugate gradient method for nonlinear optimization with application to image restoration problems

Youcef Elhamam Hemici, Samia Khelladi, Djamel Benterki (2024)

Kybernetika

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The conjugate gradient method is one of the most effective algorithm for unconstrained nonlinear optimization problems. This is due to the fact that it does not need a lot of storage memory and its simple structure properties, which motivate us to propose a new hybrid conjugate gradient method through a convex combination of $β_{k}^{R M I L}$ and $β_{k}^{H S}$ . We compute the convex parameter $θ_{k}$ using the Newton direction. Global convergence is established through the strong Wolfe conditions. Numerical experiments...

A primal-dual integral method in global optimization

Jens Hichert, Armin Hoffmann, Huan Xoang Phú, Rüdiger Reinhardt (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Using the Fenchel conjugate $F^{c}$ of Phú’s Volume function F of a given essentially bounded measurable function f defined on the bounded box D ⊂ Rⁿ, the integral method of Chew and Zheng for global optimization is modified to a superlinearly convergent method with respect to the level sequence. Numerical results are given for low dimensional functions with a strict global essential supremum.

The adaptation of the $k$ -means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm

Rudolf Scitovski, Kristian Sabo (2019)

Applications of Mathematics

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We consider the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance, whereby an ellipse $E$ is viewed as a Mahalanobis circle with center $S$ , radius $r$ , and some positive definite matrix $Σ$ . A very efficient method for solving this problem is proposed. The method uses a modification of the $k$ -means algorithm for Mahalanobis-circle centers. The initial approximation consists of the set of circles whose centers...

Exact l $_{1}$ penalty function for nonsmooth multiobjective interval-valued problems

Julie Khatri, Ashish Kumar Prasad (2024)

Kybernetika

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Our objective in this article is to explore the idea of an unconstrained problem using the exact l $_{1}$ penalty function for the nonsmooth multiobjective interval-valued problem (MIVP) having inequality and equality constraints. First of all, we figure out the KKT-type optimality conditions for the problem (MIVP). Next, we establish the equivalence between the set of weak LU-efficient solutions to the problem (MIVP) and the penalized problem (MIVP $_{ρ}$ ) with the exact l $_{1}$ penalty function. The...

Relations between multidimensional interval-valued variational problems and variational inequalities

Anurag Jayswal, Ayushi Baranwal (2022)

Kybernetika

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In this paper, we introduce a new class of variational inequality with its weak and split forms to obtain an $L U$ -optimal solution to the multi-dimensional interval-valued variational problem, which is a wider class of interval-valued programming problem in operations research. Using the concept of (strict) $L U$ -convexity over the involved interval-valued functionals, we establish equivalence relationships between the solutions of variational inequalities and the (strong) $L U$ -optimal solutions...

A penalty approach for a box constrained variational inequality problem

Zahira Kebaili, Djamel Benterki (2018)

Applications of Mathematics

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We propose a penalty approach for a box constrained variational inequality problem $(BVIP)$ . This problem is replaced by a sequence of nonlinear equations containing a penalty term. We show that if the penalty parameter tends to infinity, the solution of this sequence converges to that of $BVIP$ when the function $F$ involved is continuous and strongly monotone and the box $C$ contains the origin. We develop the algorithmic aspect with theoretical arguments properly established. The numerical results...

A stochastic mirror-descent algorithm for solving $A X B = C$ over an multi-agent system

Yinghui Wang, Songsong Cheng (2021)

Kybernetika

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In this paper, we consider a distributed stochastic computation of $A X B = C$ with local set constraints over an multi-agent system, where each agent over the network only knows a few rows or columns of matrixes. Through formulating an equivalent distributed optimization problem for seeking least-squares solutions of $A X B = C$ , we propose a distributed stochastic mirror-descent algorithm for solving the equivalent distributed problem. Then, we provide the sublinear convergence of the proposed algorithm....

Duality for a fractional variational formulation using $η$ -approximated method

Sony Khatri, Ashish Kumar Prasad (2023)

Kybernetika

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The present article explores the way $η$ -approximated method is applied to substantiate duality results for the fractional variational problems under invexity. $η$ -approximated dual pair is engineered and a careful study of the original dual pair has been done to establish the duality results for original problems. Moreover, an appropriate example is constructed based on which we can validate the established dual statements. The paper includes several recent results as special cases. ...

A new approach to solving a quasilinear boundary value problem with $p$ -Laplacian using optimization

Michaela Bailová, Jiří Bouchala (2023)

Applications of Mathematics

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We present a novel approach to solving a specific type of quasilinear boundary value problem with $p$ -Laplacian that can be considered an alternative to the classic approach based on the mountain pass theorem. We introduce a new way of proving the existence of nontrivial weak solutions. We show that the nontrivial solutions of the problem are related to critical points of a certain functional different from the energy functional, and some solutions correspond to its minimum. This idea...

Saddle point criteria for second order $η$ -approximated vector optimization problems

Anurag Jayswal, Shalini Jha, Sarita Choudhury (2016)

Kybernetika

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The purpose of this paper is to apply second order $η$ -approximation method introduced to optimization theory by Antczak [2] to obtain a new second order $η$ -saddle point criteria for vector optimization problems involving second order invex functions. Therefore, a second order $η$ -saddle point and the second order $η$ -Lagrange function are defined for the second order $η$ -approximated vector optimization problem constructed in this approach. Then, the equivalence between an (weak) efficient solution...

Locally Lipschitz vector optimization with inequality and equality constraints

Ivan Ginchev, Angelo Guerraggio, Matteo Rocca (2010)

Applications of Mathematics

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The present paper studies the following constrained vector optimization problem: ${min}_{C} f (x)$ , $g (x) \in - K$ , $h (x) = 0$ , where $f : ℝ^{n} \to ℝ^{m}$ , $g : ℝ^{n} \to ℝ^{p}$ are locally Lipschitz functions, $h : ℝ^{n} \to ℝ^{q}$ is $C^{1}$ function, and $C \subset ℝ^{m}$ and $K \subset ℝ^{p}$ are closed convex cones. Two types of solutions are important for the consideration, namely $w$ -minimizers (weakly efficient points) and $i$ -minimizers (isolated minimizers of order 1). In terms of the Dini directional derivative first-order necessary conditions for a point $x^{0}$ to be a $w$ -minimizer and first-order sufficient conditions...