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Unformatted text preview: IE411 Linear Optimization Interior Point Methods Interior Point Methods: the Breakthrough The Wall Street Journal Waits Till 1986 AT&T Patents the Algorithm, Announces KORBX What Makes LP Hard? Matrix Notation Optimality Conditions The Interior Point Paradigm Paradigm Continued Paradigm Continued The Path Following Method A Generalizable Framework Logarithmic Barrier Functions Level Sets of Logarithmic Barrier Function Lagrange Multipliers The KKT System Reduced KKT System Normal Equations: Primal Form Normal Equations: Dual Form Step Direction Decomposition is a step-toward-optimality Theorem: is a step-toward-centrality Image that c=0 and the current point were feasible is a step-toward-feasibility Find formula for primal slack vector's step directions ...
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- Fall '09