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Optimization of Computer Networks by Pablo Pavón Mariño

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Appendix BMathematical Optimization Basics

B.1 Optimization Problems

A mathematical optimization problem, or just an optimization problem, consists of finding a vector b2-math-0001 that minimizes an objective function b2-math-0002, searching only among a set of solutions that satisfy given constraints:

B.1a equation
B.1b equation
B.1c equation
B.1d equation

where b2-math-0007 are the problem decision variables1. In network optimization problems, they typically represent quantities like “capacity in a link”, “traffic to be carried through a path”, or “number of links between two nodes”. Function b2-math-0009 is called the problem objective function, (B.1b) are the equality constraints, (B.1c) the inequality constraints, and (B.1d) the set constraints.

A solution which satisfies ...

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