On the solution existence and stability of polynomial optimization problems

In this paper, we introduce and investigate a new regularity condition in the asymptotic sense for optimization problems whose objective functions are polynomial. The normalization argument analysis enables us to study existence as well stability of solutions these problems. We prove Frank–Wolfe type theorem regular an Eaves non-regular pseudoconvex Moreover, under condition, show results on such upper semicontinuity local upper-Hölder solution map polynomial At end discuss genericity condition.