Global Nonlinear Optimization Based on Eigen Analysis of Schrodinger-Type Equation

A method has been developed for deriving the approximate global optimum of a nonlinear objective function. First, the objective function is expanded into a linear equation for a moment vector, and the optimization problem is reduced to an eigen analysis problem in the wave coefficient space. Next, the process of the optimization is expressed using a Schrödinger-type equation, so global optimization is equivalent to eigen analysis of the Hamiltonian of a Schrödinger-type equation. Computer simulation of this method demonstrated that it produces a good approximation of the global optimum. An example optimization problem was solved using a Hamiltonian constructed by combining Hamiltonians for other optimization problems, demonstrating that various types of applications can be solved by combining simple Hamiltonians. key words: nonlinear, global optimization, wave function, quantum computing, Schrödinger equation