Mixed zero-one linear programming and optimal control problem
type: Item
instance of: scholarly article
title: Mixed zero-one linear programming and optimal control problem
zbMATH Open document ID: 0941.49001
published in: Bulletin of the Iranian Mathematical Society
publication date: 2000-08-07T00:00:00Z
review text: Nonlinear optimal control problems are considered. The control system is described by nonlinear differential equations with given boundary conditions. A performance index consisting of an integral function of the state and the control is to be minimized. The problem is transformed into a linear programming problem. Nonlinear functions are approximated by piecewise linear functions. The active interval is determined by \((0,1)\) variables. Therefore a mixed zero-one linear programming problem must be solved. The method is applied to a control system described by the diffusion equation and to variational problems. Computational results are presented for three numerical examples. The results are compared with known solutions. Finally, some comments on the feasibility of the problem formulation are made.
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 90C11
Mathematics Subject Classification ID: 49J20
zbMATH DE Number: 1346192
zbMATH Keywords: boundary value problems
zbMATH Keywords: separable linear programming
zbMATH Keywords: nonlinear optimal control
zbMATH Keywords: diffusion equation
author: Mehdi Radjabalipour
author: Mohammad Ali Vali
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1346192