Index sets are essential for mastering the complexity of large models. All elements in a model, such as variables, parameters, and constraints – as will be shown later on – can appear in groups, in the same way they are indexed in mathematical notation.

The convention in algebraic notation to denote a set of similar expressions is to use indexes and index sets. For example, a summation of n (numerical) terms

(1) |

is commonly abbreviated using the notation

(2) |

The expression (1) is called three-dots notation and expression (2) is called sigma-notation. Both expression are equivalent, but (2) is much shorter and more general. The later was introduced by Joseph Fourier in 1820, according to [1, p. 22]. There exist different variants of expression (2) :

(3) |

All four expressions in (3) are equivalent and they have all their advantages and disadvantages. The last notation in (3) is more general, because the index set I can be an arbitrary set defined outside the summation expression.

2.1 Exercises in the Sigma Notation

2.2 Formal Definition

2.3 Extensions

2.3.1 A list of (indexed) expressions

2.3.2 Index Sets as Expressions

2.3.3 Compound Index Notation

2.4 Exercise 1:

2.4.1 Indexed index sets

2.4.2 Ordering

2.2 Formal Definition

2.3 Extensions

2.3.1 A list of (indexed) expressions

2.3.2 Index Sets as Expressions

2.3.3 Compound Index Notation

2.4 Exercise 1:

2.4.1 Indexed index sets

2.4.2 Ordering