A primal-dual integral method in global optimization

Jens Hichert; Armin Hoffmann; Huan Xoang Phú; Rüdiger Reinhardt

Displaying similar documents to “A primal-dual integral method in global optimization”

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

Zhipeng Tu, Shu Liang (2024)

Kybernetika

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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...

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...

Combination of t-norms and their conorms

Karel Zimmermann (2023)

Kybernetika

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Non-negative linear combinations of $t_{min}$ -norms and their conorms are used to formulate some decision making problems using systems of max-separable equations and inequalities and optimization problems under constraints described by such systems. The systems have the left hand sides equal to the maximum of increasing functions of one variable and on the right hand sides are constants. Properties of the systems are studied as well as optimization problems with constraints given by the systems...

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...

Bounds on the global offensive k-alliance number in graphs

Mustapha Chellali, Teresa W. Haynes, Bert Randerath, Lutz Volkmann (2009)

Discussiones Mathematicae Graph Theory

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Let G = (V(G),E(G)) be a graph, and let k ≥ 1 be an integer. A set S ⊆ V(G) is called a global offensive k-alliance if |N(v)∩S| ≥ |N(v)-S|+k for every v ∈ V(G)-S, where N(v) is the neighborhood of v. The global offensive k-alliance number $γ ₒ^{k} (G)$ is the minimum cardinality of a global offensive k-alliance in G. We present different bounds on $γ ₒ^{k} (G)$ in terms of order, maximum degree, independence number, chromatic number and minimum degree.

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...

Interior-point method for large-scale $l_{1}$ optimization

Lukšan, Ladislav, Matonoha, Ctirad, Vlček, Jan

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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...

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...

A new look at an old comparison theorem

Jaroslav Jaroš (2021)

Archivum Mathematicum

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We present an integral comparison theorem which guarantees the global existence of a solution of the generalized Riccati equation on the given interval $[a, b)$ when it is known that certain majorant Riccati equation has a global solution on $[a, b)$ .