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Global optimization and methods for finding all the roots of systems of nonlinear algebraic equations. (Russian) Zbl 1249.65114

Summary: We propose a numerical method for finding all real roots of a system of nonlinear algebraic equations that is based on a reduction of the original problem to an equivalent auxiliary problem. Our rules for truncation of the current root of a system of nonlinear algebraic equations are similar to the rules of truncation that are used in integer programming and, with the use of necessary conditions of optimality, can also be used in iterative processes of global optimization.

MSC:

65H10 Numerical computation of solutions to systems of equations
65K05 Numerical mathematical programming methods
90C10 Integer programming
90C26 Nonconvex programming, global optimization
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