'Extreme point' presentation slideshows

Linear Programming, (Mixed) Integer Linear Programming, and Branch & Bound

Linear Programming, (Mixed) Integer Linear Programming, and Branch & Bound. COMP8620 Lecture 3-4 Thanks to Steven Waslander (Stanford) H. Sarper (Thomson Learning) who supplied presentation material. What Is a Linear Programming Problem?. Exam p le.

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Solving LP Models

Solving LP Models. Improving Search Unimodal Convex feasible region Should be successful! Special Form of Improving Search Simplex method (now) Interior point methods (later). Simple Example. Top Brass Trophy Company Makes trophies for football

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Branch-and-Cut

Branch-and-Cut. Valid inequality: an inequality satisfied by all feasible solutions Cut: a valid inequality that is not part of the current formulation Violated cut: a cut that is not satisfied by the solution to the current LP relaxation. Branch-and-Cut.

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1. Points and lines

1. Points and lines. 2. Convexity. 3. Causality. ORDINARY LINES. EXTRAORDINARY LINES?. James Joseph Sylvester. Educational Times, March 1893.

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Linear Programming

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Linear Programming

Linear Programming. Piyush Kumar (For Class of Dr. Ashok Srinivasan). Welcome to CIS5930-09. Optimization. For example. This is what is known as a standard linear program. Linear Programming. Significance A lot of problems can be converted to LP formulation

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Linear Programming

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Readings

Readings. Readings. Chapter 2 An Introduction to Linear Programming. Overview. Overview. Overview. Graphical Solutions. Graphical Solutions. Graphical Solutions. Overview

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Chapter 35 Serway & Jewett 6 th Ed.

Chapter 35 Serway & Jewett 6 th Ed. How to View Light. As a Ray. As a Wave. As a Particle. The limit of geometric (ray) optics, valid for lenses, mirrors, etc. What happens to a plane wave passing through an aperture?. Point Source Generates spherical Waves. { }. E o B o.

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Linear Programming (LP)

Linear Programming (LP). LP is simpler than NLP, hence, good for a foundation Linearity has some unique features for optimization A lot of problems are or can be converted to a LP formulation Some NLP algorithms are based upon LP simplex method. Why Talk About Linear Programming?. Given

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Chapter 2. Simplex method

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Dantzig -Wolfe Decomposition

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ISM 206 Lecture 2

ISM 206 Lecture 2. Linear Programming and the Simplex Method. Announcements. Schedule for note taking is on web (may change) First homework is on web. Announcements. Outline. Typical Linear Programming Problems Standard Form Converting Problems into standard form Geometry of LP

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C&O 355 Mathematical Programming Fall 2010 Lecture 21

C&O 355 Mathematical Programming Fall 2010 Lecture 21. N. Harvey. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box .: A A A A A A A A A A. Topics. Max Weight Spanning Tree Problem Spanning Tree Polytope Separation Oracle using Min s-t Cuts. Warning!

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Computational Geometry

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Computational Geometry

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C&O 355 Mathematical Programming Fall 2010 Lecture 18

C&O 355 Mathematical Programming Fall 2010 Lecture 18. N. Harvey. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box .: A A A A A A A A A A. Topics. Network Flow Max Flow / Min Cut Theorem Total Unimodularity Directed Graphs & Incidence Matrices

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1.4 The Extreme Point Theorem : Geometry of a linear programming problem

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