Download Presentation
Simplex Method

Loading in 2 Seconds...

1 / 9

# Simplex Method - PowerPoint PPT Presentation

Simplex Method. LP problem in standard form. Canonical (slack) form. : basic variables : nonbasic variables. Some definitions. basic solution solution obtained from canonical system by setting nonbasic variables to zero

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

## PowerPoint Slideshow about 'Simplex Method' - ostinmannual

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Simplex Method
• LP problem in standard form
Canonical (slack) form
• : basic variables
• : nonbasic variables
Some definitions
• basic solution
• solution obtained from canonical system by setting nonbasic variables to zero
• basic feasible solution
• a basic solution that is feasible
• at most
• One of such solutions yields optimum if it exists
• Adjacent basic feasible solution
• differs from the present basic feasible solution in exactly one basic variable
• Pivot operation
• a sequence of elementary row operations that generates an adjacent basic feasible solution
• Optimality criterion
• When every adjacent basic feasible solution has objective function value lower than the present solution
General steps of Simplex
• 1. Start with an initial basic feasible solution
• 2. Improve the initial solution if possible by finding an adjacent basic feasible solution with a better objective function value
• It implicitly eliminates those basic feasible solutions whose objective functions values are worse and thereby a more efficient search
• 3. When a basic feasible solution cannot be improved further, simplex terminates and return this optimal solution
Simplex-cont.
• Unbounded Optimum
• Degeneracy and Cycling
• A pivot operation leaves the objective value unchanged
• Simplex cycles if the slack forms at two different iterations are identical
• Initial basic feasible solution
Interior Point Method vs. Simplex
• Interior point method becomes competitive for very “large” problems
• Certain special classes of problems have always been particularly difficult for the simplex method
• e.g., highly degenerate problems (many different algebraic basic feasible solutions correspond to the same geometric extreme point)
Computation Steps
• 1. Find an interior point solution to begin the method
• Interior points:
• 2. Generate the next interior point with a lower objective function value
• Centering: it is advantageous to select an interior point at the “center” of the feasible region
• Steepest Descent Direction
• 3. Test the new point for optimality
• where is the objective function of the dual problem