摘要
Let f, g_1, ···, g_s be polynomials in R[X_1, ···, X_n]. Based on topological properties of generalized critical values, the authors propose a method to compute the global in?mum f~? of f over an arbitrary given real algebraic set V = {x ∈ R^n| g_1(x) = 0, ···, g_s(x) = 0}, where V is not required to be compact or smooth. The authors also generalize this method to solve the problem of optimizing f over a basic closed semi-algebraic set S = {x ∈ R^n| g_1(x) ≥ 0, ···, g_s(x) ≥ 0}.
Let f, g_1, · · ·, g_s be polynomials in R[X_1, · · ·, X_n]. Based on topological properties of generalized critical values, the authors propose a method to compute the global in?mum f~? of f over an arbitrary given real algebraic set V = {x ∈ R^n| g_1(x) = 0, · · ·, g_s(x) = 0}, where V is not required to be compact or smooth. The authors also generalize this method to solve the problem of optimizing f over a basic closed semi-algebraic set S = {x ∈ R^n| g_1(x) ≥ 0, · · ·, g_s(x) ≥ 0}.
基金
supported by the National Key Research Project of China under Grant No.2018YFA0306702
the National Natural Science Foundation of China under Grant No.11571350
