Solving Polynomial Optimization Problem and Noncooperative Games by a Homotopy Algorithm
Laura A. Kinard · TigerPrints (Clemson University) · 1987
The problem of finding all the solutions of a system of m polynomials in m variables is studied in this paper. Unlike earlier studies (6, 8, 18), optimization and game problems are the focus. This paper checks solutions, compares function evaluations whenever possible, and presents absolute error as well for future comparisons. The computer package used was HOMPACK [17], a FORTRAN implementation of a homotopy continuation algorithm. A new relaxation approach using complementarity theory to set up the first-order necessary conditions results in a system of m polynomials in m variables which subsequently can be solved by HOMPACK.