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Introduction to Optimization Neil Tang 2/23/2009

Introduction to Optimization Neil Tang 2/23/2009. Outline. Optimization Problems Mathematical Programming LP ILP CP. Optimization Problems. An optimization problem is composed of an objective function and a set of constraints.

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Introduction to Optimization Neil Tang 2/23/2009

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  1. Introduction to OptimizationNeil Tang2/23/2009 CS541 Advanced Networking

  2. Outline • Optimization Problems • Mathematical Programming • LP • ILP • CP CS541 Advanced Networking

  3. Optimization Problems • An optimization problem is composed of an objective function and a set of constraints. • Optimization problems in a graph can be solved by algorithms in graph theory. • If an optimization problem can be formulated as a Linear Programming (LP) problem, an Integer Linear Programming (ILP) problem, a Mixed Integer Linear Programming (MILP) problem or a Convex Programming (CP) problem, then the existing algorithms can be applied to solve it. CS541 Advanced Networking

  4. Mathematical Programming CS541 Advanced Networking

  5. LP LP in the standard form CS541 Advanced Networking

  6. Maximum Flow Problem - LP CS541 Advanced Networking

  7. Multi-Commodity Flow Problem - LP CS541 Advanced Networking

  8. Shortest Path Problem - ILP CS541 Advanced Networking

  9. Constrained Shortest Path Problem - ILP CS541 Advanced Networking

  10. CP CP in the standard form Property: if a local minimum exists, then it is a global minimum. CS541 Advanced Networking

  11. Rate Allocation Problem - CP CS541 Advanced Networking

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