A differentiable homotopy approach for solving polynomial optimization problems and noncooperative games (Q2641225)

A method of finding all the solutions of a system of m polynomials in m variables is studied in this paper. In contrast to earlier studies, optimization and noncooperative game problems are the focus. We develop a new relaxation approach using complementarity theory applied to first- order necessary conditions. This approach allows the solution and the proof of optimality for many difficult problems by means of a system of m polynomials in m variables, which subsequently can be solved by any method that can calculate all solutions of a polynomial system. To complete our study we apply a differentiable homotopy, check solutions, compare the number of function evaluations whenever possible, and present absolute error comparisons with other computational work.