Numerical Optimization

In the framework of the proposed continuous approach to constrained optimization problems, we describe two new solution methods which resulted from the research. The first is a continuous inexact method for solving systems of nonlinear equations and complementarity problems along the lines of the DAFNE Method, and the second is a continuous method for solving the linear programming problems along the lines of Karmarkars method which is shown to be quadratically convergent. Some numerical experience on a number of test problems is reported. Numerical Optimization, Constrained Optimization, Systems of nonlinear equations, Complementarity Problems, Linear Programming, Karmarkars method.