Why it matters

Karmarkar's algorithm changed LP landscape. Understanding shapes history.

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The architecture

Projective transformation.

Move in interior toward optimum.

Polynomial complexity.

Karmarkar's algorithmProjective transformto standard formMove in interiortoward optimumPolynomialiterations + work1984 breakthrough; drove IPM development; O(n^3.5 L) complexity
Karmarkar.
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How it works end to end

Karmarkar 1984.

Projective transformation each step.

Complexity O(n^3.5 L).

Practical for large LP.