AN UNCONSTRAINED OPTIMIZATION TECHNIQUE FOR LARGE-SCALE LINEARLY CONSTRAINED CONVEX MINIMIZATION PROBLEMS

Consider the problem of minimizing a smooth convex function f subject to the constraints Ax = b and x greater than or equal to 0, where A is an element of R(pxn). This constrained optimization problem is shown to be equivalent to a differentiable unconstrained optimization problem with 2n + p variables. This formulation of the convex constrained optimization problem can be of great advantage if n and p are large. Some preliminary numerical results are reported.