Non‐linear optimization with constraints: A cook‐book approach

Abstract Based on the stationary co‐content theorem in non‐linear circuit theory and the penalty function approach in non‐linear programming theory, a canonical circuit for simulating general non‐linear programming problems with equality and/or inequality constraints has been developed. the task of solving a non‐linear optimization problem with constraints reduces to that of finding the solution of the associated canonical circuit using a circuit simulation program, such as SPICE. A catalogue of canonical circuits is given for each class of non‐linear programming problem. Using this catalogue, an engineer can solve non‐linear optimization problems by a cook‐book approach without learning any theory on non‐linear programming. Several examples are given which demonstrate how SPICE can be used, without modification, for solving linear programming problems, quadratic programming problems, and polynomial programming problems.