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# L21 - Review of Part III Solving LP problems We learned how...

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Review of Part III: Solving LP problems We learned how to solve LP problems using the simplex method and the two-phase method. We also studied basic feasible solutions and extreme points. By now, you should be able to give the definitions of basis, basic solutions, b.f.s., convex sets, extreme points and tableau, prove the relation between b.f.s. and extreme points, explain why we focus on b.f.s., determine optimal solution or unboundedness, prove optimality and unboundedness algebraically, construct auxiliary problems and determine feasibility of LP problems, prove infeasibility algebraically.

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CO350 Linear Programming Chapter 8: Degeneracy and Finite Termination 20th June 2005
Chapter 8: Finite Termination 1 Motivation In the next 2 weeks, we aim at proving Fundamental Theorem of Linear Programming. For any LP problem, exactly one of the following is true: 1. it has an optimal solution; 2. it is infeasible; 3. it is unbounded. The main tool: two-phase method . Upon successful completion of the two-phase method, we have one of the above three conclusions [Moreover, we have algebraic proofs of each of them.] We only need to ensure the successful completion of sim- plex method. We shall see that degeneracy may prevent the successful completion of simplex method; perturbing the LP can remove degeneracy; using appropriate choice rules for leaving variables can ensure successful completion.

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Chapter 8: Finite Termination 2 Degeneracy A simple proof that the simplex method will stop: There are a finite number of feasible bases (at most n choose m ).
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L21 - Review of Part III Solving LP problems We learned how...

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