Linear programming with entropic perturbation

Abstract

In this paper, we derive an unconstrained convex programming approach to solving standard form linear programs through an entropic perturbation. The whole duality theory is established by using only one simple inequality “lnz ≤ z −1 forz > 0”. A curved search algorithm is also proposed for obtaining a pair of primal and dualε-optimal solutions. The proposed algorithm is proven to be globally convergent with a quadratic rate of convergence. Computational results are included in support of theoretic findings.