From continuous to discrete

Abstract

One approach that has been used to solve the DGP is to represent it as a continuous optimization problem [59]. To understand it, we consider a DGP with K = 2, V = {u, v, s}, E = {{ u, v}, {v, s}}, where the associated quadratic system is [Formula presented] which can be rewritten as [Formula presented] Consider the function f: ℝ6→ ℝ, defined by [Formula presented] It is not hard to realize that the solution x∗∈ ℝ6 of the associated DGP can be found by solving the following problem: [Formula presented] That is, we wish to find the point x*∈ ℝ6 which attains the smallest value of f.