Solving Nonlinear Optimization Problems by Means of the Network Programming Method
Vladimir N. BURKOV
network programming, nonlinear optimization, dual problem, integer linear programming
We suggest a new approach to solve discrete optimization problems, based on the possibility of presenting a function as a superposition of simpler functions. Such a superposition can be easily represented in the form of a network for which the inputs correspond to variables, intermediate nodes – to functions entering the superposition, and in the final node the function is calculated. Due to such representation the method has been called the method of network programming (in particular, dichotomic). The network programming method is applied for solving nonlinear optimization problems. The concept of a dual problem is implemented. It is proved that the dual problem is a convex programming problem. Necessary and sufficient optimality conditions for a dual problem of integer linear programming are developed.