An Algorithm for Convex Quadratic Programming That Requires O(n3.5L) Arithmetic Operations

A new interior point method for minimizing a convex quadratic function over a polytope is developed. We show that our method requires O ( n 3.5 L ) arithmetic operations. In our algorithm we construct a sequence P z 0 , P z 1 , …, P z k , … of nested convex sets that shrink towards the set of optimal solution(s). During iteration k we take a partial Newton step to move from an approximate analytic center of P z k − 1 to an approximate analytic center of P z k . A system of linear equations is solved at each iteration to find the step direction. The solution that is available after O (√ mL ) iterations can be converted to an optimal solution. Our analysis indicates that inexact solutions to the linear system of equations could be used in implementing this algorithm.