introduction to optimization neil tang 2 23 2009 n.
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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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Presentation Transcript
outline
Outline
  • Optimization Problems
  • Mathematical Programming
  • LP
  • ILP
  • CP

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optimization problems
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.

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mathematical programming
Mathematical Programming

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slide5
LP

LP in the standard form

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maximum flow problem lp
Maximum Flow Problem - LP

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multi commodity flow problem lp
Multi-Commodity Flow Problem - LP

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shortest path problem ilp
Shortest Path Problem - ILP

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slide10
CP

CP in the standard form

Property: if a local minimum exists, then it is a global minimum.

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rate allocation problem cp
Rate Allocation Problem - CP

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