A finite algorithm for global minimization of separable concave programs

Researchers first examined the problem of separable concave programming more than thirty years ago, making it one of the earliest branches nonlinear programming to be explored. This paper proposes a new finite algorithm for solving this problem. In addition to providing a proof of finiteness, the paper discusses a new way of designing branch-and-bound algorithms for concave programming that ensures finiteness. The algorithm uses domain reduction techniques to accelerate convergence; it solves problems with as many as 100 concave variables, 400 linear variables and 50 constraints in about five minutes on an IBM RS/6000 Power PC.