Everything about The Ellipsoid Method totally explained
The
ellipsoid method is an
algorithm for solving
convex optimization problems. It was introduced by
Naum Z. Shor, Arkady Nemirovsky, and David B. Yudin in 1972, and used by
Leonid Khachiyan to prove the
polynomial-time solvability of linear programs. At the time, the ellipsoid method was the only algorithm for solving linear programs whose runtime was provably polynomial. However, the
interior-point method and variants of the
simplex algorithm are much faster than the ellipsoid method, in both theory and practice. The algorithm works by enclosing the minimizer of a
convex function in a sequence of ellipsoids whose volume decreases at each iteration.
Description
A convex optimization problem consists of a convex function
for all feasible
.
Application to Linear Programming
Performance
The ellipsoid method is rarely used in practice due to poor practical performance and is used almost exclusively as an educational tool to prove the polynomial complexity of linear programs.
Further Information
Get more info on 'Ellipsoid Method'.
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