Filled function method for nonlinear equations

AbstractSystems of nonlinear equations are ubiquitous in engineering, physics and mechanics, and have myriad applications. Generally, they are very difficult to solve. In this paper, we will present a filled function method to solve nonlinear systems. We will first convert the nonlinear systems into equivalent global optimization problems with the property: x∗ is a global minimizer if and only if its function value is zero. A filled function method is proposed to solve the converted global optimization problem. Numerical examples are presented to illustrate our new techniques

Security Steiner’s Inequality on Layering Functions

The classical definition of Steiner symmetrizations of functions are defined according to the Steiner symmetrizations of function level sets and the layered representation of functions. In this paper, the definition is not only transformed into Steiner symmetrizations of one-dimensional parabolic functions, but also depends on the Steiner symmetrizations of the level sets of log-concave functions. To this end we prove Steiner’s inequality on layering functions in the space of log-concave functions