Transcription of III. Solving Linear Programs by Interior-Point Methods
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III. Solving Linear Programs by Interior-Point Methods
Optimization MethodsDraft of August 26, Linear Programsby Interior-Point MethodsRobert FourerDepartment of Industrial Engineering and Management SciencesNorthwestern UniversityEvanston, Illinois 60208-3119, (847) 4er/Copyrightc 1989 2004 Robert FourerB 72 Optimization Methods of August 26, 2005B 7310. Essential FeaturesSimplex Methods get to the solution of a Linear program by moving fromvertex to vertex along edges of the feasible region. It seems reasonable thatsome better method might get to an optimum faster by instead moving throughtheinteriorof the region, directly toward the optimal point. This is not as easyas it sounds, in other respects the low-dimensional geometry of Linear Programs can bemisleading.
Draft of August 26, 2005 B–75 We can regard the interior points (x,¯ π,¯ σ)¯ of this system to be those that satisfy the inequalities strictly: x >¯ 0, σ >¯ 0. Our goal is to show how interior-point methods can generate a series of such points that tend toward a solution of the
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