Solving a class of non-convex quadratic problems based on generalized KKT conditions and neurodynamic optimization technique

Alaeddin Malek; Najmeh Hosseinipour-Mahani

The search session has expired. Please query the service again.

Displaying similar documents to “Solving a class of non-convex quadratic problems based on generalized KKT conditions and neurodynamic optimization technique”

New results on semidefinite bounds for $ℓ_{1}$ -constrained nonconvex quadratic optimization

Yong Xia (2013)

RAIRO - Operations Research - Recherche Opérationnelle

Similarity:

In this paper, we show that the direct semidefinite programming (SDP) bound for the nonconvex quadratic optimization problem over unit ball (QPL1) is equivalent to the optimal d.c. (difference between convex) bound for the standard quadratic programming reformulation of QPL1. Then we disprove a conjecture about the tightness of the direct SDP bound. Finally, as an extension of QPL1, we study the relaxation problem of the sparse principal component analysis, denoted by...

A globally convergent neurodynamics optimization model for mathematical programming with equilibrium constraints

Soraya Ezazipour, Ahmad Golbabai (2020)

Kybernetika

Similarity:

This paper introduces a neurodynamics optimization model to compute the solution of mathematical programming with equilibrium constraints (MPEC). A smoothing method based on NPC-function is used to obtain a relaxed optimization problem. The optimal solution of the global optimization problem is estimated using a new neurodynamic system, which, in finite time, is convergent with its equilibrium point. Compared to existing models, the proposed model has a simple structure, with low complexity....

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

Zhipeng Tu, Shu Liang (2024)

Kybernetika

Similarity:

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...

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

Similarity:

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.

Derivatives of Hadamard type in scalar constrained optimization

Karel Pastor (2017)

Kybernetika

Similarity:

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 $ℓ$ -stable at feasible point functions. Then we show the advantages of obtained results with respect to the previously obtained results.

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

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

Kybernetika

Similarity:

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...

Simultaneous routing and flow rate optimization in energy-aware computer networks

Przemysław Jaskóła, Piotr Arabas, Andrzej Karbowski (2016)

International Journal of Applied Mathematics and Computer Science

Similarity:

The issue of energy-aware traffic engineering has become prominent in telecommunications industry in the last years. This paper presents a two-criteria network optimization problem, in which routing and bandwidth allocation are determined jointly, so as to minimize the amount of energy consumed by a telecommunication infrastructure and to satisfy given demands represented by a traffic matrix. A scalarization of the criteria is proposed and the choice of model parameters is discussed...

Locally Lipschitz vector optimization with inequality and equality constraints

Ivan Ginchev, Angelo Guerraggio, Matteo Rocca (2010)

Applications of Mathematics

Similarity:

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...

The Placement of Electronic Circuits Problem: A Neural Network Approach

M. Ettaouil, K. Elmoutaouakil, Y. Ghanou (2010)

Mathematical Modelling of Natural Phenomena

Similarity:

The goal of this paper is to apply the Continuous Hopfield Networks (CHN) to the Placement of Electronic Circuit Problem (PECP). This assignment problem has been expressed as Quadratic Knapsack Problem (QKP). To solve the PECP via the CHN, we choose an energy function which ensures an appropriate balance between minimization of the cost function and simultaneous satisfaction of the PECP constraints. In addition, the parameters of this ...