Introduction to Optimization Neil Tang 2/23/2009

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# Introduction to Optimization Neil Tang 2/23/2009 - PowerPoint PPT Presentation

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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### Introduction to OptimizationNeil Tang2/23/2009

Outline
• Optimization Problems
• Mathematical Programming
• LP
• ILP
• CP

Optimization Problems
• An optimization problem is composed of an objective function and a set of constraints.
• 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.

Mathematical Programming

LP

LP in the standard form

Maximum Flow Problem - LP

Multi-Commodity Flow Problem - LP

Shortest Path Problem - ILP