A new potential reduction algorithm for smooth convex programming

This paper extends and analyzes a new potential reduction algorithm for solving smooth convex programming. Under a kind of strict feasibility assumption, we show that the algorithm under modification requires a total of O((ρ - n)ℓ) number of iterations, and the total arithmetic operations are not more than O(n³ℓ), where n + √2n ≤ ρ ≤ 2n and ℓ is the initial input size. As an application to usual linear or convex quadratic programming, this algorithm solves the pair of primal and dual problems in at most O((ρ - n)L) iterations, and the total arithmetic operations are shown to be of the order of O(n³L), where L is the input size.