ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
The paper presents an extended approach to non-linear first-order approximation of non-linear programming problems and it explains how to transform an approximate problem into a strictly convex one. The essence of the proposed approximation technique is to rewrite each given function hj as a composite gj o Ψj. The function Ψj has to be chosen - the paper explains how to do this - while gj is linear approximated with gj. The approximation of hj is then obtained as gj o Ψj.This approach enables one to obtain approximate functions with variable conservativeness, which implies an adjustable approximate problem. A solution procedure, which replaces the original problem with a sequence of approximate problems, can therefore adjust each succeeding approximate problem to improve the convergence properties.The theory is illustrated with a three parameters controlled approximation. This technique represents, together with an optimality criteria based solution procedure, a powerful and economic tool for solving nonlinear programming problems. The three parameters, which influence to a great extent the conservativeness of the approximate functions, are under full control of the optimizer. They are varied automatically during the process of optimization to speed-up the convergence or to prevent oscillations.The benefits gained from the proposed approach are demonstrated on several numerical examples involving structures and a dynamic multibody system.
Additional Material:
7 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620330202
