Mathematics

# MATH 7234: Optimization and Complexity

Lecture - 4 credits

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CE

- Offers theory and methods of maximizing and minimizing solutions to various types of problems.
- Studies combinatorial problems including mixed integer programming problems (MIP); pure integer programming problems (IP); Boolean programming problems; and linear programming problems (LP).
- Topics include convex subsets and polyhedral subsets of n-space; relationship between an LP problem and its dual LP problem, and the duality theorem; simplex algorithm, and Kuhn-Tucker conditions for optimality for nonlinear functions; and network problems, such as minimum cost and maximum flow-minimum cut.
- Also may cover complexity of algorithms; problem classes P (problems with polynomial-time algorithms) and NP (problems with nondeterministic polynomial-time algorithms); Turing machines; and NP-completeness of traveling salesman problem and other well-known problems.

Offers theory and methods of maximizing and minimizing solutions to various types of problems.

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