Finding All Minimizing Points of Bi-quadratic Surface by Set-oriented Branching

Take-Yuki Nagao


Non-linear optimization, B-Spline, Spline Interpolation, Box Constrained Optimization


There are many useful iterative methods for optimization, but there are global optimization problems that can not be solved by iterative methods and non-iterative methods are required for such problems. In this article, a novel and non-iterative approach is presented for finding all the minimizing points of two-dimensional bi-quadratic spline surface under a box constraint. It is shown that the feasible set can be divided into finitely many branches according to the properties of the objective function and that the problem of finding all the minimizing points can be reduced to a finite combination of one dimensional solvable optimization problems. The idea of choosing the branches according to the structure of the objective function is detailed and a transformation of the objective function is proposed for the reduction of the problem dimension.

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