"This thesis investigates several non-linear analogues of Lagrange functions in the hope of answering the question 'Is it possible to generalise Lagrange functions such that they may be applied to a range of nonconvex objective problems?' The answer to this question is found to be yes for a particular class of optimization problems. Furthermore the thesis asserts that in derivative free optimization the general schema which is most theoretically and practically appealing involves the reformulation of both objective and constraint functions, whilst the least practically successful approach for everything but the most simple convex case is the augmented Lagrangian approach." / Doctor of Philosophy

"This thesis investigates several non-linear analogues of Lagrange functions in the hope of answering the question 'Is it possible to generalise Lagrange functions such that they may be applied to a range of nonconvex objective problems?' The answer to this question is found to be yes for a particular class of optimization problems. Furthermore the thesis asserts that in derivative free optimization the general schema which is most theoretically and practically appealing involves the reformulation of both objective and constraint functions, whilst the least practically successful approach for everything but the most simple convex case is the augmented Lagrangian approach." / Doctor of Philosophy

M. Tech. Mathematical Technology. / Discusses the main problems in terms of how to derive mathematical models for a free, a forced and a damped spring pendulum and determining numerical solutions using a computer algebra system (CAS), because exact analytical solutions are not obvious. Hence this mini-dissertation mainly deals with how to derive mathematical models for the spring pendulum using the Euler-Lagrange equations both in the Cartesian and polar coordinate systems and finding solutions numerically. Derivation of the equations of motion are done for the free, forced and damped cases of the spring pendulum. The main objectives of this mini-dissertation are: firstly, to derive the equations of motion governing the oscillatory and rotational components of the spring pendulum for the free, the forced and damped cases of the spring pendulum ; secondly, to solve these equations numerically by writing the equations as initial value problems (IVP); and finally, to introduce a novel way of incorporating nonlinear damping into the Euler-Lagrange equations of motion as introduced by Joubert, Shatalov and Manzhirov (2013, [20]) for the spring pendulum and interpreting the numerical solutions using CAS-generated graphics.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Includes bibliographical references (p. 263-266).