Displaying similar documents to “Optimality conditions for an interval-valued vector problem”

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...

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 ) - K , h ( x ) = 0 , where f : n m , g : n p are locally Lipschitz functions, h : n q is C 1 function, and C m and K 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...

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...

Derivatives of Hadamard type in scalar constrained optimization

Karel Pastor (2017)

Kybernetika

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Vsevolod I. Ivanov stated (Nonlinear Analysis 125 (2015), 270-289) the general second-order optimality condition for the constrained vector problem in terms of Hadamard derivatives. We will consider its special case for a scalar problem and show some corollaries for example for -stable at feasible point functions. Then we show the advantages of obtained results with respect to the previously obtained results.

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.

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...

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...