Search

Abstract: In this paper, we extend the filled function method proposed in Lin et al. (2009) [10] to solve the constrained system of nonlinear equations, and we propose two methods to find a solution of such a system. Finally the efficiency of the present method is illustrated through some examples. [Copyright &y& Elsevier]

Abstract: A new proof of the Mahler conjecture in is given. In order to prove the result, we introduce a new method — the vertex removal method; i.e., for any origin-symmetric polygon , there exists a linear image contained in the unit disk , and there exist three contiguous vertices of lying on the boundary of . We can show that the volume-product of decreases when we remove the middle vertex of the three vertices. [ABSTRACT FROM AUTHOR]

Abstract: Systems 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: 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. [Copyright &y& Elsevier]

Abstract: In this paper, a new global optimization approach based on the filled function method is proposed for solving box-constrained systems of nonlinear equations. We first convert the nonlinear system into an equivalent global optimization problem, and then propose a new filled function method to solve the converted global optimization problem. Several numerical examples are presented and solved by using different local minimization methods, which illustrate the efficiency of the present approach. [Copyright &y& Elsevier]