Difference between revisions of "Interior-point method for LP"

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(Introduction)
(Introduction)
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Date Presented: May 25, 2014 <br>
 
Date Presented: May 25, 2014 <br>
 
=Introduction=
 
=Introduction=
Interior point methods are a type of algorithm that are used in solving both linear and nonlinear convex optimization problems that contain inequalities as constraints. The LP Interior-Point method relies on having a linear programming model with the objective function and all constraints being continuous and twice continuously differentiable.
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Interior point methods are a type of algorithm that are used in solving both linear and nonlinear convex optimization problems that contain inequalities as constraints. The LP Interior-Point method relies on having a linear programming model with the objective function and all constraints being continuous and twice continuously differentiable. The problem is solved (assuming there IS a solution) either by iteratively solving for Karun-Kush-Tucker (KKT) conditions or to the original problem with equality instead of inequality constraints, and then applying Newton's method to these conditions.
  
 
=Uses=
 
=Uses=

Revision as of 15:33, 25 May 2014

Authors: John Plaxco, Alex Valdes, Wojciech Stojko. (ChE 345 Spring 2014)
Steward: Dajun Yue, Fengqi You
Date Presented: May 25, 2014

Contents

Introduction

Interior point methods are a type of algorithm that are used in solving both linear and nonlinear convex optimization problems that contain inequalities as constraints. The LP Interior-Point method relies on having a linear programming model with the objective function and all constraints being continuous and twice continuously differentiable. The problem is solved (assuming there IS a solution) either by iteratively solving for Karun-Kush-Tucker (KKT) conditions or to the original problem with equality instead of inequality constraints, and then applying Newton's method to these conditions.

Uses

Algorithm

Example

Conclusion

Sources

1. R.J. Vanderbei, Linear Programming: Foundations and Extensions (Chp 17-22). Springer, 2008.
2. J. Nocedal, S. J. Wright, Numerical optimization (Chp 14). Springer, 1999.
3. S. Boyd, L. Vandenberghe, Convex Optimization (Chp 11). Cambridge University Press, 2009