Engineering Optimization: Theory and Practice, Fourth Edition

2 Introduction to Optimization

Figure 1.1 Minimum off (x)is same as maximum of−f (x).

cf(x)

cf(x)

f(x)

f(x)

f(x)

f(x) f(x)

cf*

f* f*

x* x x* x

c + f(x)

c + f*

Figure 1.2 Optimum solution ofcf (x)orc+f (x)same as that off (x).

Table 1.1 lists various mathematical programming techniques together with other

well-defined areas of operations research. The classification given in Table 1.1 is not

unique; it is given mainly for convenience.

Mathematical programming techniques are useful in finding the minimum of a

function of several variables under a prescribed set of constraints. Stochastic process

techniques can be used to analyze problems described by a set of random variables

having known probability distributions. Statistical methods enable one to analyze the

experimental data and build empirical models to obtain the most accurate represen-

tation of the physical situation. This book deals with the theory and application of

mathematical programming techniques suitable for the solution of engineering design

problems.