Optimization Methods and Applications

by Yang, Xiaoqi; Teo, K. L.; Caccetta, Lou

• ISBN13: 9780792368663
• ISBN10: 0792368665
• Format: Hardcover
• Copyright: 2001-05-01
• Publisher: Kluwer Academic Pub

Summary

The book includes chapters on optimal control, nonlinear programming, global optimization, network optimization, and dynamic systems, dealing with theory, computational techniques and real-world applications. For the application chapters, the topics involved are optimum digital Laguerre network, stochastic optimal control model of solar powered car, personnel task scheduling problem, envelope constrained filter design and optimal steel casting. For practitioners, postgraduate students and researchers in optimization and optimal control.

Table of Contents

Preface	xi
An Appreciation of Professor N.U. Ahmed	xiii
A Publication List of Professor N.U. Ahmed	xvii
Part I OPTIMAL CONTROL
Practical Stability of Impulsive Delay Differential Equations and Applications to Control Problems	3	(20)
George Ballinger
Xinzhi Liu
Introduction	4	(1)
Preliminaries	4	(2)
Main Results	6	(4)
Application	10	(13)
References	21	(2)
A Review of Ill-Conditioning and Regularization in Optimal Control Computation	23	(22)
Francis Benyah
Les S. Jennings
Introduction	24	(1)
Optimal Control Problem Template for MISER3	25	(1)
Control Parametrization	26	(1)
State Discretization Methods	27	(3)
Condition Numbers for Constrained Optimization	30	(2)
Test Problem 1	32	(3)
Regularization of Optimal Control Problems	35	(4)
Test Problem 2: The Container Crane Problem	39	(1)
Conclusions	40	(5)
References	42	(3)
Worst-Case Optimal Regulation of Linear Systems in the Presence of Structured Perturbations	45	(20)
Saroj K. Biswas
M. Bala Subrahmanyam
Introduction	46	(1)
Problem Statement	47	(3)
Optimal Solution	50	(7)
Computation of Disturbance Rejection Capacity	57	(1)
Examples	58	(3)
Conclusions	61	(4)
References	61	(4)
True Proportional Navigation System with Acceleration Saturation Constraint	65	(16)
Cheng-Chew Lim
Mingyan Li
Introduction	66	(1)
System Model	66	(2)
Saturation Constraint Analysis	68	(6)
Observability with Saturation Constraint	74	(2)
Simulation Results	76	(3)
Conclusions	79	(2)
References	79	(2)
Evaluation of Penalty Functions for Optimal Control	81	(24)
Rein Luus
Wichaya Mekarapiruk
Colin Storey
Introduction	82	(1)
Problem Formulation	82	(2)
Iterative Dynamic Programming (IDP)	84	(2)
Numerical Results	86	(14)
Concluding Remarks	100	(5)
References	102	(3)
On the Optimal Control Systems with Multiple Controllers	105	(20)
Katsumi Moriwaki
Introduction	106	(1)
Optimal Regulator and Preliminaries	107	(2)
LQR Problem with 2 Controllers	109	(6)
Controllers Decoupling via Internally Balanced State Space Representations	115	(3)
Numerical Examples and Discussions	118	(4)
Conclusion	122	(3)
References	123	(2)
Multilevel Optimization of Optimal Control Problems	125	(14)
Volker Rehbock
Introduction	126	(2)
General Problem	128	(1)
Multilevel Approach	128	(3)
Implementation	131	(2)
Numerical Results	133	(3)
Parallel Implementation	136	(1)
Conclusions	137	(2)
References	138	(1)
Modified Direct Gradient Descent Control of Nonlinear Systems	139	(12)
K. Shimizu
S. Ito
K. Otsuka
Introduction	140	(1)
Direct Gradient Descent Control	140	(2)
Modified Direct Gradient Descent Control	142	(2)
Simulation	144	(2)
Concluding Remarks	146	(5)
References	146	(2)
Appendix: Stability	148	(3)
Computation of Feedback Control for Infinite Time Optimal Control Problems	151	(16)
K.H. Wong
G. Peter
Introduction	152	(1)
Problem Statement	153	(1)
The Approximation Problem (P(T))	153	(1)
Synthesizing the Optimal Feedback Control Law for the Approximate Problem (P(T))	154	(2)
Interpolation using a Cubic Spline Approach on the Fitting Domain DT	156	(1)
Creating an Approximate Problem Using Cubic Spline Feedback Structure on the Domain DT	157	(1)
Properties of Asymptotic Stability of the Optimal Control Feedback Control of the Problem (Q)	158	(1)
Finite Time Approximation to the Problem (Q)	159	(1)
A Practical Example	159	(8)
References	163	(4)
Part II OPTIMIZATION METHODS
A Homogenized Cutting Plane Method to Solve the Convex Feasibility Problem	167	(24)
E. D. Andersen
J. E. Mitchell
C. Roos
T. Terlaky
Introduction	168	(1)
Barrier functions and proximity measures	169	(2)
A column generation method	171	(4)
Choosing a restart point	175	(3)
Global convergence	178	(1)
An implementation	179	(6)
Computational results	185	(3)
Conclusions	188	(3)
References	189	(2)
Algorithms for Some Hard Knapsack Problems	191	(28)
Louis Caccetta
Araya Kulanoot
Introduction	192	(3)
Preliminaries	195	(2)
Subset Sum Problem (SSP)	197	(4)
Strongly Correlated Problem (SCKP)	201	(4)
Inverse Strongly Correlated Knapsack Problem (ISCKP)	205	(2)
Bounded Knapsack Problem (BKP)	207	(7)
Conclusions	214	(5)
References	214	(5)
Non-Static Network Optimization Problems: A Survey	219	(28)
X. Cai
D. Sha
C. K. Wong
Introduction	220	(1)
The Non-Static Network Flow Model	220	(4)
Non-Static Shortest Path Problems	224	(3)
Non-Static Maximum Flow Problems	227	(3)
Non-Static Minimum Cost Flow Problems	230	(3)
Non-Static Vehicle Routing Problems	233	(3)
Other Non-Static Network Optimzation Problems	236	(1)
Conclusions	237	(10)
References	238	(9)
Asymptotic Rates of Convergence of SQP-Type Methods of Feasible Directions	247	(20)
Michael M. Kostreva
Xibin Chen
Introduction	248	(2)
Definitions and Propositions	250	(4)
Asymptotic Rate of Convergence	254	(8)
Comparison of Convergence Rates	262	(1)
Conclusions	263	(4)
References	264	(3)
Nonlinear Lagrangian Methods in Constrained Nonlinear Optimization	267	(12)
Duan Li
Xiaolin Sun
Introduction	268	(2)
p-th Power Lagrangian Method	270	(1)
Minimax-type Lagrangian Function	271	(3)
Logarithmic-Exponential Lagrangian Function	274	(2)
Conclusions	276	(3)
References	276	(3)
Parallel Algorithms for Solving Large-Scale Nonlinear Optimization Problems	279	(16)
Paul Kang-Hoh Phua
Daohua Ming
Weiguo Fan
Yan Zhang
Conventional Methods for Nonlinear Optimization	280	(1)
Parallel Quasi-Newton Algorithms	281	(3)
Vectorization and Fine-tuning Techniques	284	(4)
Computational Results	288	(7)
References	293	(2)
Second Order Strict Converse Duality in Nonlinear Fractional Programming	295	(14)
Xin Min Yang
Kok Lay Teo
Xiaoqi Yang
Introduction and Preliminaries	296	(2)
Second Order Strict Converse Duality I	298	(4)
Second Order Strict Converse Duality II	302	(7)
References	305	(4)
Part III OPTIMIZATION APPLICATIONS
Chebyshev Optimization of Circular Arrays	309	(12)
Mattias Dahl
Ingvar Claesson
Sven Nordebo
Sven Nordholm
Introduction	310	(1)
Problem Formulation	311	(1)
The Complex Chebyshev Approximation Problem as a Semi-Infinite Linear Program	312	(1)
Semi-Infinite Linear Programming	313	(2)
Brief Outline of Linear Programming	315	(1)
Numerical Example	316	(1)
Summary	317	(4)
References	317	(4)
Optimum Pole Position for Digital Laguerre Network with Least Square Error Criterion	321	(10)
H. H. Dam
Kok Lay Teo
Yanqun Liu
S. Nordebo
Introduction	322	(1)
Problem Formulation	322	(2)
Optimization Method	324	(2)
Simulation Studies	326	(2)
Conclusions	328	(3)
References	329	(2)
A Markov Model for the Stochastic Optimal Control of a Solar Powered Car	331	(12)
Phil Howlett
Introduction	332	(1)
Formulation	332	(1)
A Recursive Equation for the Optimal Controls	333	(3)
The Properties of the Optimal Controls	336	(2)
Some Elementary Examples	338	(3)
Conclusions	341	(2)
References	341	(2)
The Personnel Task Scheduling Problem	343	(26)
Mohan Krishnamoorthy
Andreas T Ernst
Introduction	344	(1)
The PTSP	344	(4)
Variants of the PTSP	348	(9)
Literature Review	357	(2)
Applications	359	(3)
Test Data	362	(4)
Conclusions	366	(3)
References	367	(2)
Envelope Constrained Filter Design: Robustness Issues	369	(30)
B. Vo
A. Cantoni
Introduction	370	(2)
Envelope Constrained Filtering	372	(8)
Robustness Issues	380	(15)
Conclusions	395	(4)
References	395	(4)
A Robust Numerical Algorithm for the Optimal Control of Heat Transfer in the Continuous Casting of Steel	399	(1)
Y.H. Wu
M. Chuedoung
G. Zhang
Introduction	400	(1)
Heat Transfer Model	401	(2)
Statement of the Optimal Control Problem	403	(1)
Numerical Method for the Optimal Control Problem	404	(2)
Numerical Approximation of the Jacobian Matrix	406	(1)
Numerical Algorithm	407	(1)
An Illustrative Example	408	(2)
Conclusions	410	(1)
References	411