نتایج جستجو برای: convex semi

تعداد نتایج: 195136  

2006
Emil Ernst Michel Théra

In this note we prove that an extended-real-valued lower semi-continuous convex function Φ defined on a reflexive Banach space X achieves its supremum on every nonempty bounded and closed convex set of its effective domain Dom Φ, if and only if the restriction of Φ to Dom Φ is sequentially continuous with respect to the weak topology on the underlying space X .

2012
Alfredo N. Iusem Daniel Reem Benar F. Svaiter

A remarkable recent result by S. Artstein-Avidan and V. Milman states that, up to precomposition with affine operators, addition of affine functionals, and multiplication by positive scalars, the only fully order preserving mapping acting on the class of lower semicontinuous proper convex functions defined on Rn is the identity operator, and the only fully order reversing one acting on the same...

Journal: :CoRR 2018
Dongruo Zhou Pan Xu Quanquan Gu

We propose a stochastic variance-reduced cubic regularized Newton method for non-convex optimization. At the core of our algorithm is a novel semi-stochastic gradient along with a semi-stochastic Hessian, which are specifically designed for cubic regularization method. We show that our algorithm is guaranteed to converge to an ( , √ )-approximately local minimum within Õ(n/ ) second-order oracl...

2008
Francesca Prinari

Fixed a bounded open set Ω of R , we completely characterize the weak* lower semicontinuity of functionals of the form F (u,A) = ess sup x∈A f(x, u(x), Du(x)) defined for every u ∈ W 1,∞(Ω) and for every open subset A ⊂ Ω. Without a continuity assumption on f(·, u, ξ) we show that the supremal functional F is weakly* lower semicontinuous if and only if it can be represented through a level conv...

Journal: :Math. Program. 2002
Mohit Tawarmalani Nikolaos V. Sahinidis

We define a convex extension of a lower-semicontinuous function to be a convex function that is identical to the given function over a pre-specified subset of its domain. Convex extensions are not necessarily constructible or unique. We identify conditions under which a convex extension can be constructed. When multiple convex extensions exist, we characterize the tightest convex extension in a...

Journal: :J. Global Optimization 2004
Samir Adly Emil Ernst Michel Théra

Closed convex sets for which the barrier cone has a nonempty interior, as well as proper extended-values real functionals for which the domain of their Fenchel conjugate is nonempty, are mathematical objects currently encountered in various areas of optimization theory and variational analysis (see for instance the class of well-behaved functions introduced by Auslender and Crouzeix in [5]). Th...

Journal: :Int. J. Math. Mathematical Sciences 2005
Jian-Wen Peng Xinmin Yang

Throughout this paper, we use intA and CoA to denote the interior and the convex hull of a set A, respectively. Let I be an index set. For each i ∈ I , let Yi, Ei be two Hausdorff topological vector spaces. Consider a family of nonempty convex subsets {Xi}i∈I with Xi ⊆ Ei. Let X = ∏ i∈I Xi and E = ∏ i∈I Ei. An element of the set Xi = ∏ j∈I\i Xi will be denoted by xi; therefore, x ∈ X will be wr...

Journal: :Dissertationes Mathematicae 2002

Journal: :ESAIM: Control, Optimisation and Calculus of Variations 2008

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