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Nonlinear Parameter Optimization Using R Tools by John C. Nash

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Chapter 1Optimization problem tasks and how they arise

In this introductory chapter we look at the classes of problems for which we will discuss solution tools. We also consider the interrelationships between different problem classes as well as among the solution methods. This is quite general. R is only incidental to this chapter except for some examples. Here we write our list of things to do.

1.1 The general optimization problem

The general constrained optimization problem can be stated as follows.

  1. Find x = c01-math-0001(x)
  2. such that
  3. (x)>= 0

Note that c01-math-0002 is a scalar function but c01-math-0003 is a vector. There may or may not be constraints on the values of c01-math-0004, and these are expressed formally in the vector of functions c01-math-0005. While these functions are general, many problems have much simpler constraints, such as requirements that the values of c01-math-0006 be no less than some lower bounds or no greater than some upper bounds ...

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