The homogeneous and self - dual model and algorithm for linear optimization

instead of (1). Clearly, (3) is a homogeneous LP and is self-dual which essentially follows from the constraints form a skew-symmetric system. The interpretation of (3) is τ is a homogenizing variable and the constraints represent primal feasibility, dual feasibility, and reversed weak duality. The homogeneous model (3) was first studied by Goldman and Tucker [2] in 1956 and they proved (3) always has a nontrivial solution (x∗, y∗, τ∗) satisfying xjs ∗ j = 0, x ∗ j + s ∗ j > 0, ∀j, τ∗κ∗ = 0, τ∗ + κ∗ > 0, (4)