Ilan Adler

Interior path following primal-dual algorithms. Part I: Linear programming

AbstractWe describe a primal-dual interior point algorithm for linear programming problems which requires a total of

A polynomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension

O\left( {\sqrt n L} \right)

Limiting behavior of the affine scaling continuous trajectories for linear programming problems

number of iterations, whereL is the input size. Each iteration updates a penalty parameter and finds the Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem. The algorithm is based on the path following idea.

A geometric view of parametric linear programming

AbstractWe describe a primal-dual interior point algorithm for convex quadratic programming problems which requires a total of

Two-settlement electricity markets with price caps and Cournot generation firms

O\left( {\sqrt n L} \right)

The equivalence of linear programs and zero-sum games

number of iterations, whereL is the input size. Each iteration updates a penalty parameter and finds an approximate Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem. The algorithm is based on the path following idea. The total number of arithmetic operations is shown to be of the order of O(n3L).