Algorithmic and Computational Aspects of Composite Concave Programming

In this paper we discuss the algorithmic and computational aspects of the parametric nonlinear optimization method c-programming. Our objective in looking at the method from this vantage point is twofold. First, to explain more clearly where c-programming sits in optimization theory. Second, to throw more light on the details of the collaboration that it forges with other optimization methods. The first objective is accomplished through an analysis of c-programming'ys genealogy. The latter is achieved by an examination of the basic structure of c-programming algorithms, and by reporting on extensive numerical experiments conducted with c-programming algorithms in collaboration with linear programming and dynamic programming techniques. These experiments very convincingly show that c-programming has the ability to significantly expand the scope of linear programming, dynamic programming, and possibly other optimization methods.