systems of equations

Global Optimization of Non-Linear Systems of Equations by Simulating the Flight of a Projectile in the Conformational Space

  • Nick Harkiolakis
    • Categories Applications - Science and Engineering, Global Optimization, Nonlinear Optimization Tags , , , ,

    A new heuristic optimization algorithm is presented based on an analogy with the physical phenomenon of a projectile launched in a conformational space under the influence of a gravitational force. Its implementation simplicity and the option to enhance it with local search methods make it ideal for the optimization of non-linear systems of equations. The … Read more

    New quasi-Newton method for solving systems of nonlinear equations

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , , , , ,

    In this report, we propose the new Broyden method for solving systems of nonlinear equations, which uses the first derivatives, but it is more efficient than the Newton method (measured by the computational time) for larger dense systems. The new method updates QR decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires $O(n^2)$ … Read more

    Global Optimization of Non-Linear Systems of Equations by Simulating the Flight of a Projectile in the Conformational Space

  • Nicholas Harkiolakis
    • Categories Nonlinear Optimization, Optimization Software and Modeling Systems, Stochastic Approaches Tags , , , , ,

    A new heuristic optimization algorithm is presented based on an analogy with the physical phenomenon of a projectile launched in a conformational space under the influence of a gravitational force. Its implementation simplicity and the option to enhance it with local search methods make it ideal for the optimization of non-linear systems of equations. The … Read more