**Reviews**

Below are some reviews published since the first edition
appeared in 1988.

" The
writer of a textbook has a conflict to resolve. On
the one hand it is desirable to include in the textbook
material that would be of interest to the widest audience,
whereas on the other hand it is desirable to insertmaterial
close to the author’s heart. The first edition
of Papalambros and Wilde’s *Principles of
Optimal Design* leaned in the direction of emphasis
on material close to the heart of the authors, in
particular, monotonicity analysis. The second edition
improves the balance, and the result is a textbook
that should be useful to a much wider audience. The
new Chapter 2, Model Construction, includes popular
topics, and the old specialized Chapter 6, Global
Bound Construction, which also included geometric
programming, is gone. There are still some popular
topics that are left out or shortchanged, but this
is difficult to avoid without greatly expanding the
thickness and cost of the textbook. The second edition
is available in paperback, and at the list price of
$44.95 it is a bargain. On the day I checked on the
Web, I could get it from Barnes and Noble with a coupon
for $42.90 including FedEx shipping.

The second edition
retains and strengthens some of the excellent features
of the first. These include a wealth of good examples,
solved in detail and well illustrated, as well as
very nice illustrations of various concepts of optimization.
The Notation section at the beginning of the book
is useful, and every chapter ends with a Notes section
that provides information on additional sources of
material. There is also a large number of homework
problems in each chapter. The book is well written
and easy to follow and provides an excellent basis
for a first graduate course on design optimization
in Mechanical Engineering, Aerospace Engineering,
or Mechanics departments.

The division of
material surprised me at first. In particular, some
search methods for unconstrained and constrained problems
are discussed in Chapters 4 and 5, respectively. Others
are given in Chapter 7, entitled Local Computation.
On second thought, I could see the benefit of this
arrangement, as it allows the teacher to more easily
skip algorithmic descriptions. Indeed, I find that,
as the years pass, I tend to teach fewer and fewer
algorithms in my optimization classes because of the
increasing availability of good software.

A brief description
of the contents of the book follows: Chapter 1,Optimization
Models, discusses the important topic of the formulation
of the optimization problem. As the authors say in
the preface, “a good model can make optimization
almost trivial, whereas a bad one can make correct
optimization difficult or impossible.” Compared
to the first edition, this chapter now has material
on multicriterion optimization as well as expanded
coverage of hierarchical models.

Chapter 2, Model
Construction, is a new chapter that includesmaterial
on fitting models from data, originally in Chapter
1, but now with kriging methods and neural networks
added. The chapter also includes a good treatment
of natural and practical constraints. Chapter 3, Model
Boundedness, begins with a very thorough discussion
of the effects of constraints on optima and continues
with monotonicity analysis.

Chapter 4, Interior
Optima, provides mostly theoretical aspects of unconstrained
optimization, including optimality conditions and
the concept of convexity. Numericalmethods in this
chapter are limited to steepest descent and Newton’s
method, as well as a general discussion of trust region
algorithms. More methods are discussed in Chapter
7. Chapter 5, Boundary Optima, includes optimality
conditions but also the gradient projection and generalized
reduced gradient methods, as well as linear programming.
I would have liked to see more in this chapter on
sensitivity of optimal solutions to problem parameters.
Chapter 6, Parametric and Discrete Optima, is mostly
about the use of monotonicity theory for model reduction,
like Chapter 5 from the first edition. There is much
more on discrete variables but not with standard methods,
like branch and bound for linear problems, or stochastic
methods, such as genetic algorithms.

Chapter 7, Local
Computation, includes search algorithms for constrained
and unconstrained optimization. Compared to the first
edition, it includes trust regions and convex approximations.
The absence of the conjugate gradient method is conspicuous
(even though quasi-Newton is there). I would have
also liked to see methods that do not require derivatives,
such as pattern search methods. Chapter 8, Principles
and Practice, describes the calculation of derivatives,
scaling, problem formulations, checklists, and a road
map of where to find things in the book, as well as
lists of software and Internet sites."

**- Raphael T. Haftka, University of Florida,
AIAA Journal Vol. 39, No. 7, July 2001 **

" The
book written by professors Panos Y. Papalambros and
Douglas J. Wilde on the principles of optimal design
is a very useful course both to students and practicing
engineers. The continuing push for reducing design
costs and cycle time using computer-based models makes
the use of optimization tools inevitable.

The book is organized into eight chapters. Chapter
1 presents an introduction in the basic concepts as
system, mathematical model, optimization design etc.
There are defined the well posed problems for that
the feasibility and boundedness are discussed. The
global and local optima are introduced and the chapter
is concluded with a discussion of the dependency between
modeling and computation.

In Chapter 2, after a brief review of curve fitting,
regression analysis, neural networks and kriging,
some very useful and interesting modeling-examples
are given, in order to illustrate the concepts introduced
before.

Chapter 3 contains an in-depth treatment of the methods
concerning with model reduction and verification process.
The bounds and the impact of constraints upon them
are the target of a careful identifying process. A
significant reduction in model size both increases
the designer's understanding of the problem and eases
the subsequent computational effort.

In the Chapters 4 and 5 the classical theory of differential
optimization is developed, starting with the derivation
optimality conditions and than showing how iterative
algorithms can be naturally constructed from them.
The basic ideas for optimality of constrained problems
are explored. Starting from the optimality conditions,
some basic search procedures that can be used to reach
optima through numerical iteration are derived.

Chapter 6 analyzes how optimal designs are affected
by changes in the design environment defined by problem
parameters. Special and original emphasis fell on
monotonicity analysis application to construct parametric
routines that generate optimal designs, with a minimum
of iterative searching.

The local search algorithms are discussed in Chapter
7. The influences and limitations that can affect
the numerical optimization are emphasized and, finally,
a small number of considered preferable methods are
described. Remarkable is the use of active set strategies
in local computation, in direct analogy with the case
decomposition and global computation.

Chapter 8, focused on optimization practice, summarizes
the tactics in conducting practical design studies.
Containing also a very useful checklist, this final
chapter shows the experience of the authors and makes
the book more attractive for design project work.

A special attention is given to the clarity in exposition.
In order to give a rigorous proof of principles, the
new concepts definitions are followed by immediate
applications to simple examples. Each chapter ends
with proposed exercises and the figures are both clear
and concise.

This book is undoubtedly a valuable reference for
students, academics, researchers, and industrial engineers
interested in optimization design. It can be characterized,
as a comprehensive and self-contained exposition,
which would arm the reader with all the relevant tools,
required for analyzing, modeling and computing in
the optimization practice."

**-
Dorin LUCACHE, IASI POLYTECHNIC MAGAZINE,
Vol. 13, No. 3-4**

"
This is a text book for a one-semester course
in optimal design. It is suitable for seniors or first
year graduate students. It can also be used by researchers
concerned with design, operations research and many
other areas in which computers are heavily used for
designs and planning. Classical optimization theory
and numerical algorithms are integrated with the newer
ideas of monotonicity analysis and model boundedness.
While the book has a heavy engineering flavor this
should not discourage others from its use."

** - Mathematics & Computers in Simulation,
Vol. 31, 1989**

"
This book grew out of courses given at the
University of Michigan and Stanford University to
an audience coming from engineering sciences. Its
flavour is thus in this spirit, and it may - in considerable
part also by its many examples which are worked out
- be of interest to mathematicians which have to give
lectures to such a community or to work on such topics."

**-
H.Muthsam, Padiatrie und Padologie (Wien) 5th of Feb.
1989**

" This is an
excellent book for anyone interested in modeling,
model building, optimization of models, and the interaction
between optimization and the modeling process. It
combines classical optimization theory with new ideas
of monotonicity and model boundedness that provide
valuable information for determining the most efficient
and correct formulation of a model. This book is definitely
aimed at the engineering design students, and it will
be a valuable addition to the libraries of operation
researchers, economists, numerical analysts and some
computer scientist. However, it ma appear little uninspiring
for physicists and mathematicians because of its strong
engineering flavor, and honest simplicity throughout.
There are eight chapters in the book, each of which
has a concise introduction to set the stage for the
concepts to be discussed, and a summary which re-enforces
and ties all the ideas presented. The first seven
chapters discuss mathematical modeling, different
types of models, model boundedness, interior optima,
boundary optima, Karush-Kuhn-Tucker conditions, global
bound construction and some discussion on non-linear
problems. The Chapter 8 reviews modeling techniques
and approaches presented in the previous seven chapters.
The optimization checklist included in this chapter
should also provide good help to student readers.

Overall this appears
to be a good, comprehensive textbook for senior level
undergraduate engineering students. The equations
and illustrations are also adequate. However, some
advanced researchers in the physical science may find
this book uninteresting and uninspiring mainly because
of its content and the way it is presented."

**-
Wooil M. Moon, Physics in Canada, Vol. 46, Jul. 1990**

"
This book is concerned with the analysis and
solution of models that represent an engineering device.
Its philosophy is that an engineering model, before
plunging into the uncertain area of numerical computation
to solve a non-linear program, increases the likelihood
of finding an optimal solution to the design problem.
The proposed analyses aim to identify the relevant
variables and critical constraints, to check that
the model is feasible and bounded, and discuss approaches
to simplifying the model. These methods are discussed
in Chapters 1 to 6, and in Chapter 7 a small number
of non-linear programming algorithms are described.
Chapter 8 presents a checklist of issues that should
be addressed by anyone, design engineer or not, concerned
with building and solving a mathematical model.

This textbook is
suitable for a final year undergraduate course; it
assumes knowledge of linear algebra and differential
calculus. There are exercises at the end of each chapter."

**-
S. Powell, International Statistical Reviews**

"
The present (interesting and important) book
deals with optimization as well as with the modeling
process. As sources of the book the authors mention
WILDE's monograph "Globally Optimal Design"
(1978) and graduate engineering design course at the
University of Michigan and the Stanford University.
Comparing with the first source the authors emphasized
more precise, explicit, and broader treatment and
many examples for the support of understanding. Each
chapter is finished by a section "Summary. Notes.
Exercises". Unfortunately, no solutions are offered
concerning these exercises. It is the declared intention
of the authors to integrate the (classical) optimization
theory and numerical methods with the newer concepts
of monotonicity analysis and model boundedness in
order to establish a procedure of design optimization
where global analysis and local iterative methods
are really integrated.

Chapter 1 "Optimization
models" includes fundamental notions and stresses
mathematical modeling, the optimal design concept,
different kinds of optima, question of modeling data,
and the connection between solution and computation.

Chapter 2 "Model
boundedness", where bounds, extrema, and optima,
the constrained optimum, underconstrained models,
the way to well bounded models are included. Beyond
monotonicity, inequality and equality constraints
and the model preparation procedure will be discussed.

Chapter 3 "Interior
optima" is devoted to fundamental notions of
optimization such as the existence of optima, local
approximation, optimality, convexity, local exploration
(descent), searching along a line, and stabilization.

Chapter 4 "Boundary
optima" deals with feasible directions, tangency,
equality constraints, the Hessian, feasible iterations,
inequality constraints, Karush-Kuhn-Tucker conditions,
linear programming, and sensitivity.

Chapter 5 "Model
reduction": parametric solution, the monotonicity
table, hidden monotonicity, the activity map, overconstrained
models, finding the optimal case, starting case selections,
discrete variables.

Chapter 6 "Global
bound constructions" treats geometric programming,
where the geometric inequality, unconstrained and
constrained geometric inequality, unconstrained and
constrained geometric programming problems (including
duality) are considered.

Chapter 7 "Local
computation" contains local and global convergence,
single variable minimization, quasi-Newton methods,
finite differences and scaling, active set strategies,
penalties and barriers, sequential quadratic programming.

Chapter 8 "Principles
and practices", at the end of the book, tries
to summarize and to organize theories and techniques
of the previous chapters with the aim to get a problem-solving
strategy as a guidance in practical design optimizations.
Thus modeling consideration prior to computation and
for local computation and moreover, an optimization
checklist and finally a review with respect to concepts,
rules and principles are given.

The book is supplemented
by an extensive reference list and an author list.

To summarize: we recommend highly this book not only
for engineering students but for operations analysts,
economists, and all those who are interested on (applied)
optimization. "

**-
K.H. Elster and R. Tichatsohk, Optimization, Vol.
20, 1989 **

"
The availability of cheap, powerful computers, together
with the promise of artificial intelligence has drawn
the attention of engineering designers and others
to the subject of modeling - the mathematical description
of physical or economical description of a physical
or economic system. A natural purpose of modeling
is optimization - finding the best value for some
goal associated with the model.

This is therefore a text book about modeling
for design optimization and the mutual interaction
between these two processes. It presents a condensed
version of classical optimization theory and numerical
algorithms, which it integrates with the newer ideas
of monotonicity analysis and model boundedness."

**-
Engineering Designer,1989**

"
This book is primarily intended for engineering and
applied science graduate students, and possibly upper
level seniors. It is furthermore intended for use
in a course which covers the theoretical principles
and applications of engineering design optimization.
Sufficient worked example problems are included. It
would also serve very nicely for use by practicing
engineering with an interest in optimal design. While
the example problems are predominantly oriented towards
mechanical engineering design applications this text
book could also be adapted for use in other engineering
disciplines including civil, industrial, chemical,
and manufacturing engineering.

The book begins with a treatise on models for
engineering design optimization and stresses the importance
of properly posed, hierarchically structured models.
The authors go on to discuss the unified interplay
of modeling and computation in optimization, and continue
to carry this concept throughout the book.

The concepts related to the mathematics necessary
to achieve model boundedness are covered next, and
the groundwork for the important concept of monotonicity
analysis is laid down. Constraint activity, the concept
of cases as subsets of an overall optimization problem,
and constraint criticality and constraint relaxation
conditions are discussed. The author's first and second
monotonicity principles are also included. These principles
are of significant importance in recognizing a (1)
well constrained objective function and (2) characteristics
associated with variables in the constraints (nonobjective
variables) possessing relevance (ie, occurring in
an active constraint). It is important to note that
the authors speak from first hand experience when
discussing this topic since it represents a currently
active research direction for them. At the conclusion
of the second chapter they succinctly describe in
summary form the manner in which the concepts discussed
can and should be systematically applied to real problem
if problem size reduction is to be successfully achieved.
A more detained discussion of model reduction follows
in chapter 5.

Optimum solutions lying within (rather than on)
the boundaries of the design space occupy the next
topic of discussion in the book. Necessary and sufficient
conditions are covered through the use of vector calculus.
The concepts of convexity and convex functions are
described, followed by a discussion of first-order
gradient following techniques and second-order algorithms
(Newton's methods) which employ the Hessian matrix.
This chapter, in effect, concentrates on the solution
of unconstrained optimization problems.

Optima lying on (rather than within) the boundary
of the feasible regions, and algorithms capable of
locating them comprise the next topic of discussion.
The authors address the questions "What happens
if the optimization problem includes constraints and
the objective function has a minimum on a boundary?"
and "What are the appropriate optimality conditions
for constrained problem that can be operationally
useful without explicitly eliminating constraints?"
Definition of, and explanations for, the concepts
of feasible directions, feasible perturbations, and
the feasible domain are given and graphically depicted.
The classical mathematical formulation of the constrained
optimization problems is developed.

Included among the topics covered are Lagrange
multipliers, the constrained Hessian and its relation
to curvature at the boundary of the feasible region,
and techniques such as GRG and gradient projection
which guarantee feasible iterations while simultaneously
decreasing the objective function. The Krush-Kuhn-Tucker
(KKT) conditions satisfying the necessary optimality
conditions for a problem containing equality and inequality
constraints are described and geometrically interpreted.
Finally, concepts behind linear programming (LP) problems
are discussed along with algorithms for solving problems
of this type, and the chapter concludes with mention
of sensitivity analysis.

Acquiring information germane to model reduction or
-as the authors call it- case decomposition, is discussed
in chapter 5. This is important for efficiency regions
since it is applied prior to the implementation of
any numerical iterative calculations. The authors
discuss numerous approaches for "steering through
a small fraction of well bounded cases, activating
or relaxing constraints until further local improvement
to the optimum solution is no longer possible."
Included among these approaches are the use of the
monotonicity table (MT); a systematic approach for
keeping track of the reasoning processes involved
in detecting and eliminating underconstrained cases
based on monotonicity analysis; and the activity map
for detecting and screening out overconstrained cases.
Activity mapping when combined with the use of monotonicity
tables are useful for organizing well-constrained
cases and displaying their iterelations. The authors
go on to discuss the Maximal activity principle for
studying the consistency of constraints, and a heuristic
referred to as the Coincidence rule which provides
guidelines for selecting good starting cases for the
location of the optimum in a tractable number of iterations.

In Local computation (chapter 7) the authors
provide an appreciation of what is involved in numerical
optimization and they describe a few methods that
are considered to work reasonably well within the
limits of current understanding of these methods.
The concepts of local and global convergence are defined,
where the former corresponds to efficiency of an algorithm
and the latter corresponds to the robustness of an
algorithm. Quasi-Newton methods, methods which rely
on Hessian matrix update techniques, and the classic
DFP and BFGS algorithms are included. The use of finite
difference calculus and variable scaling is also discussed
as are Lagrange multiplier estimates and penalty function
methods. The chapter concludes with a summary of sequential
quadratic programming. The final chapter covers what
the author term "principles and practice."
Two optimization checklists are provided which offer
guidance for the systematic solution of optimization
problems. That is quite useful.

This reviewer strongly
recommends that engineering faculty adopt textbook
for a course they may teach on design optimization.
The authors, being leaders in a number of important
and timely topics in the area of design optimization
research (particularly monotonicity analysis), provide
a modern presentation of the mathematics and computational
aspect of design optimization in a manner which flows
smoothly and is enjoyable to read. Readers particularly
interested in the subject of design optimization will
find the book to be extremely interesting and difficult
to put aside as the authors build the concepts of
optimization in a gradual and logical manner.

It is exciting to
find a "fresh" approach to design optimization
such as is discussed in this book. It is hoped that
through this book the authors can inspire new researchers
to seek new challenges, and to explore new areas that
have the potential to lead to new techniques and discoveries
in the field of design optimization. Current concern
for worldwide competitiveness in manufactured goods
should, in part, provide the necessary incentive for
the pursuit of new developments in the field of design
optimization, while books like this one can provide
a firm background in the principles of optimization
which are necessary to explore new areas holding significant
promise such as knowledge-based programming, machine
learning, and expert system.

* Principle of
Optimal Design: Modeling and Computation* has
been well designed and thought out, and the authors
are to be congratulated on their fine contribution
to the field of engineeing design optimization. One
expects that many students will benefits from the
knowledge they will acquire from this book. One last
comment concerning optimization software is in order.
While the reviewer understands and sympathizes with
the authors' intent to emphasize underlying principles
rather than numerical details, he hopes that as this
textbook begins to be used in engineeing optimization
courses throughout the world that interested faculty
would pool the software subroutines developed in their
courses into a library (these could be sent to the
authors or the publisher) which could serve as a basis
for an educational optimization software library to
be included with the textbook or made available by
the publisher. Oftentimes, the amount of time required
to develop such subroutines from scratch exceeds the
time available in a one semester course. This would
also add more of the computer aided "flavor"
to the book."

**-
David A. Hoeltzel, Applied Mechanics Reviews, Vol.
42, No. 6, 1989**

"
Explains the concept of optimal design and
demonstrates the relationship between the mathematical
model that describes a design and the solution methods
that optimize it. This second edition takes into account
developments in computer power and optimization, and
includes a discussion of trust region and convex approximation
algorithms. A new chapter focuses on how to construct
optimal design models. The final chapter on optimization
practice has been expanded to include computation
of derivatives, interpretation of algorithmic results,
and selection of algorithms and software."

**-
Book News, Inc. (from Amazon.com)**

"
Textbook puts the concept of optimal design
on a rigorous foundation and demonstrates the intimate
relationship between the mathematical model that describes
a design and the solution methods that optimize it.
This edition has been thoroughly updated to reflect
new developments. Softcover; hardcover also available.
DLC: Mathematical optimization."

**-
Book Info (from Amazon.com)**

"
Since the first edition was published, computers
have become ever more powerful, design engineers are
tackling more complex systems, and the term "optimization"
is now routinely used to denote a design process with
increased speed and quality. This second edition takes
account of these developments and brings the original
text thoroughly up to date. The book now discusses
trust region and convex approximation algorithms.
A new chapter focuses on how to construct optimal
design models. Three new case studies illustrate the
creation of optimization models. The final chapter
on optimization practice has been expanded to include
computation of derivatives, interpretation of algorithmic
results, and selection of algorithms and software."

**-
Book Description (from Amazon.com)**

.