A generalized computing paradigm based on artificial dynamic models for mathematical programming
type: Item
instance of: scholarly article
title: A generalized computing paradigm based on artificial dynamic models for mathematical programming
zbMATH Open document ID: 1332.90264
author: N. E. Zubov
published in: Soft Computing
publication date: 2015-12-02T00:00:00Z
review text: The authors consider nonlinear equation systems of the form \[ g_i(x) = 0, i = 1, \dots, N, \] where \(g_i:\mathbb R^n \to\mathbb R\) are continuously differentiable functions. The traditional approach to such problems, which minimizes the sum of the squared residuals may fail in the presence of singularities of the Jacobian matrix or if the initial solution guess is far away from the solution of the given problem. To overcome these difficulties, the authors propose to formulate a generic programming problem by a proper set of ordinary differential equations, whose equilibrium points correspond to the solutions of the given problem. The proposed method is described, its asymptotic stability is demonstrated. Effectiveness of the proposed approach is shown on numerical results presented in the concluding part of the paper.
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 6515282
zbMATH Keywords: dynamic system theory
zbMATH Keywords: nonlinear systems of equations
zbMATH Keywords: non-linear optimization problems
zbMATH Keywords: Lyapunov theory
reviewed by: Karel Zimmermann
MaRDI profile type: Publication
full work available at URL: s00500-013-1162-z
OpenAlex ID: W1979788254
cites work: An interior point method for general large-scale quadratic programming problems
cites work: A Class of Methods for Solving Nonlinear Simultaneous Equations
cites work: A survey of recent developments in multiobjective optimization
cites work: Trust Region Methods
cites work: Q5313725
cites work: Sizing and Least-Change Secant Methods
cites work: On the bridge between combinatorial optimization and nonlinear optimization: a family of semidefinite bounds for 0--1 quadratic problems leading to quasi-Newton methods
cites work: Survey of multi-objective optimization methods for engineering
cites work: Q4840578
cites work: Reference direction approach for solving multiple objective nonlinear programming problems
cites work: Q5652137
DOI: 10.1007/S00500-013-1162-Z
description: scientific article; zbMATH DE number 6515282