Continuity of Minima: Local Results

نویسندگان

  • Eugene A. Feinberg
  • Pavlo O. Kasyanov
چکیده

This paper compares and generalizes Berge’s maximum theorem for noncompact image sets established in Feinberg, Kasyanov and Voorneveld [5] and the local maximum theorem established in Bonnans and Shapiro [3, Proposition 4.4].

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Spurious Local Minima are Common in Two-Layer ReLU Neural Networks

We consider the optimization problem associated with training simple ReLU neural networks of the form x 7→ ∑k i=1 max{0,w> i x} with respect to the squared loss. We provide a computer-assisted proof that even if the input distribution is standard Gaussian, even if the dimension is unrestricted, and even if the target values are generated by such a network, with orthonormal parameter vectors, th...

متن کامل

Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued ma...

متن کامل

Completing river networks with only partial river observations via hydrology-aware ODETLAP

Fragmentary river segments have to be joined appropriately before becoming useful to addressing transportation problems like route planning and pollutant tracking. When height observations are available at the given river locations only, conventional terrain reconstruction techniques often fail to help to classify river/non-river locations at the tributaries. We propose using the hydrology-awar...

متن کامل

Global Well-posedness for the Critical 2d Dissipative Quasi-geostrophic Equation

We give an elementary proof of the global well-posedness for the critical 2D dissipative quasi-geostrophic equation. The argument is based on a non-local maximum principle involving appropriate moduli of continuity.

متن کامل

Integral functionals on Sobolev spaces having multiple local minima

THEOREM A. Let (X, τ) be a Hausdorff topological space and Ψ : X →]−∞,+∞], Φ : X → R two functions. Assume that there is r > infX Ψ such that the set Ψ (]−∞, r]) is compact and first-countable. Moreover, suppose that the function Φ is bounded below in Ψ(]−∞, r]) and that the function Ψ+ λΦ is sequentially lower semicontinuous for each λ ≥ 0 small enough. Finally, assume that the set of all glob...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015