lecture 1 - Math 482 (Lecture 1): Introduction Today: we...

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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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lecture 1 - Math 482 (Lecture 1): Introduction Today: we...

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