Quadratic growth and critical point stability of semi-algebraic functions
نویسندگان
چکیده
We show that quadratic growth of a semi-algebraic function is equivalent to strong metric subregularity of the subdifferential — a kind of stability of generalized critical points. In contrast, this equivalence can easily fail outside of the semi-algebraic setting.
منابع مشابه
A Method for Solving Convex Quadratic Programming Problems Based on Differential-algebraic equations
In this paper, a new model based on differential-algebraic equations(DAEs) for solving convex quadratic programming(CQP) problems is proposed. It is proved that the new approach is guaranteed to generate optimal solutions for this class of optimization problems. This paper also shows that the conventional interior point methods for solving (CQP) problems can be viewed as a special case of the n...
متن کاملA Semi-Algebraic Approach for the Computation of Lyapunov Functions
In this paper we deal with the problem of computing Lyapunov functions for stability verification of differential systems. We concern on symbolic methods and start the discussion with a classical quantifier elimination model for computing Lyapunov functions in a given polynomial form, especially in quadratic forms. Then we propose a new semi-algebraic method by making advantage of the local pro...
متن کاملOn the quadratic support of strongly convex functions
In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.
متن کاملA fixed point approach to the stability of additive-quadratic-quartic functional equations
In this article, we introduce a class of the generalized mixed additive, quadratic and quartic functional equations and obtain their common solutions. We also investigate the stability of such modified functional equations in the non-Archimedean normed spaces by a fixed point method.
متن کاملQuadratic $alpha$-functional equations
In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Math. Program.
دوره 153 شماره
صفحات -
تاریخ انتشار 2015