to obtain an approximate second-order KKT solution of the `p-norm models in polynomial time with a fixed error tolerance, and then test our `p-norm models on CRSP(1992-2013) and also S&P 500 (2008-2012) data. The empirical results illustrate that our `p-norm regularized models can generate portfolios of any desired sparsity with portfolio variance, portfolio return and Sharpe Ratio comparable t...

We consider the problem of estimating change in the dependency structure between two p-dimensional Ising models, based on respectively n1 and n2 samples drawn from the models. The change is assumed to be structured, e.g., sparse, block sparse, node-perturbed sparse, etc., such that it can be characterized by a suitable (atomic) norm. We present and analyze a norm-regularized estimator for direc...

Normed Space [1, 2, §2]. A norm ‖·‖ on a linear space (U ,F) is a mapping ‖·‖ : U → [0,∞) that satisfies, for all u,v ∈ U , α ∈ F , 1. ‖u‖ = 0 ⇐⇒ u = 0. 2. ‖αu‖ = |α| ‖u‖. 3. Triangle inequality: ‖u+ v‖ ≤ ‖u‖+ ‖v‖. A norm defines a metric d(u,v) := ‖u− v‖ on U . A normed (linear) space (U , ‖·‖) is a linear space U with a norm ‖·‖ defined on it. • The norm is a continuous mapping of U into R+. ...

Using s-norm S, we introduce the notion of sensible fuzzy R-subgroups in near-rings, and some related properties are investigated. Mathematics Subject Classification: 06F35, 03G25, 03E72.

Under one-sided conditions, we establish explicit expressions for the condition numbers of core inverse and solution a linear system, using Hartwig Spindelb?ck?s decomposition, spectral norm Frobenius norm. We also present structured perturbation inverse.

We establish a general operator parallelogram law concerning a characterization of inner product spaces, get an operator extension of Bohr’s inequality and present several norm inequalities. More precisely, let A be a C∗ -algebra, T be a locally compact Hausdorff space equipped with a Radon measure μ and let (At)t∈T be a continuous field of operators in A such that the function t → At is norm c...

On the basis of the concept of interval valued intuitionistic fuzzy set introduced by K. Atanassov [3], the notion of interval valued intuitionistic fuzzy subsemigroup (ideal, bi-ideal, (1, 2)-ideal) of a semigroup with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help o...

Consider a function u defined on Rn, except, perhaps, on a closed set of potential singularities S. Suppose that u solves the eikonal equation ‖Du‖ = 1 in the pointwise sense on Rn \S, where Du denotes the gradient of u and ‖ · ‖ is a norm on Rn with the dual norm ‖ · ‖∗. For a class of norms which includes the standard p-norms on Rn, 1 < p < ∞, we show that if S has Hausdorff 1-measure zero an...

In this article, we design a novel linearized and momentum-preserving Fourier pseudo-spectral scheme to solve the Rosenau-Korteweg de Vries equation. With aid of new semi-norm equivalence between method finite difference method, prior bound numerical solution in discrete L ∞ $$ {L}^{\infty } -norm is obtained from momentum conservation law. Subsequently, based on energy solution, show that, wit...