Math 482 (Lecture 1): Introduction
Today: we will discuss (roughly) Section 1.1 and 2.1 of the textbook
1. What is Mathematical Optimization?
*
Mathematical optimization
is the study of
algorithms
to maximize (or minimize) an
objective function
over a
feasible region
.
Examples:
Objective function="profit", "love match", "personal interest" (the last two are
intentionally ambiguous)
Examples:
Feasible region defined by "resources", "available partners", "time"
Key issue:
How to convert ambiguity into
mathematical programs
?
 Algorithms can be controversial
"Real" people care: (three searches)
Searched for jobs in "Mathematical optimization"
and for "linear programming"
and finally my own research area:
"algebraic combinatorics"
2. What is Linear Programming?
* Linear programming is the case of mathematical optimization where the
 objective function is defined by a linear function (in many variables); and
 the feasible region is defined by linear inequalities and equalities
Wikipedia gives a good overview of the main ideas
Some history.
Culture of this material/course:
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 Spring '08
 Staff
 Math, Linear Programming, Optimization, McDonald, Mathematical optimization, objective function, feasible region

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