Search results for "APPROXIMATION"
showing 10 items of 818 documents
A novel technique for stochastic root-finding: Enhancing the search with adaptive d-ary search
2017
The most fundamental problem encountered in the field of stochastic optimization, is the Stochastic Root Finding (SRF) problem where the task is to locate an unknown point x∗ for which g(x∗) = 0 for a given function g that can only be observed in the presence of noise [15]. The vast majority of the state-of-the-art solutions to the SRF problem involve the theory of stochastic approximation. The premise of the latter family of algorithms is to oper ate by means of so-called “small-step”processesthat explorethe search space in a conservative manner. Using this paradigm, the point investigated at any time instant is in the proximity of the point investigated at the previous time instant, render…
ε-Regularized two-level optimization problems: Approximation and existence results
2006
The purpose of this work is to improve some results given in [12], relating to approximate solutions for two-level optimization problems. By considering an e-regularized problem, we get new properties, under convexity assumptions in the lower level problems. In particular, we prove existence results for the solutions to the e-regularized problem, whereas the initial two-level optimization problem may fail to have a solution. Finally, as an example, we consider an approximation method with interior penalty functions.
Approximation by mappings with singular Hessian minors
2018
Let $\Omega\subset\mathbb R^n$ be a Lipschitz domain. Given $1\leq p<k\leq n$ and any $u\in W^{2,p}(\Omega)$ belonging to the little H\"older class $c^{1,\alpha}$, we construct a sequence $u_j$ in the same space with $\operatorname{rank}D^2u_j<k$ almost everywhere such that $u_j\to u$ in $C^{1,\alpha}$ and weakly in $W^{2,p}$. This result is in strong contrast with known regularity behavior of functions in $W^{2,p}$, $p\geq k$, satisfying the same rank inequality.
Geometry of spaces of compact operators
2008
We introduce the notion of compactly locally reflexive Banach spaces and show that a Banach space X is compactly locally reflexive if and only if $\mathcal{K}(Y,X^{**})\subseteq\mathcal{K}(Y,X)^{**}$ for all reflexive Banach spaces Y. We show that X * has the approximation property if and only if X has the approximation property and is compactly locally reflexive. The weak metric approximation property was recently introduced by Lima and Oja. We study two natural weak compact versions of this property. If X is compactly locally reflexive then these two properties coincide. We also show how these properties are related to the compact approximation property and the compact approximation prope…
Asymptotic Equivalence of Difference Equations in Banach Space
2014
Conjugacy technique is applied to analysis asymptotic equivalence of nonautonomous linear and semilinear difference equations in Banach space.
Some kind of Bishop-Phelps-Bollobás property
2016
In this paper we introduce two Bishop–Phelps–Bollobas type properties for bounded linear operators between two Banach spaces X and Y: property 1 and property 2. These properties are motivated by a Kim–Lee result which states, under our notation, that a Banach space X is uniformly convex if and only if the pair (X,K) satisfies property 2. Positive results of pairs of Banach spaces (X,Y) satisfying property 1 are given and concrete pairs of Banach spaces (X,Y) failing both properties are exhibited. A complete characterization of property 1 for the pairs (lp,lq) is also provided.
Solution of coupled riccati equations occurring in nash games
2006
To obtain the open-loop Nash strategy for a linear-quadratic differential game, a set of coupled matrix Riccati equations has to be solved. It is shown that by means of algebraic transformations, the original problem can be reduced to another one to which the successive approximation method is applicable. This leads to a simple iterative algorithm with a predetermined approximation error. An example is given to illustrate the proposed method.
Computing continuous numerical solutions of matrix differential equations
1995
Abstract In this paper, we construct analytical approximate solutions of initial value problems for the matrix differential equation X ′( t ) = A ( t ) X ( t ) + X ( t ) B ( t ) + L ( t ), with twice continuously differentiable functions A ( t ), B ( t ), and L ( t ), continuous. We determine, in terms of the data, the existence interval of the problem. Given an admissible error e, we construct an approximate solution whose error is smaller than e uniformly, in all the domain.
Competing species system as a qualitative model of radiation therapy
2016
To examine complex features of tumor dynamics we analyze a competing-species lattice model that takes into account the competition for nutrients or space as well as interaction with therapeutic factors such as drugs or radiation. Our model might be interpreted as a certain prey–predator system having three trophic layers: (i) the basal species that might be interpreted as nutrients; (ii) normal and tumor cells that consume nutrients, and (iii) therapeutic factors that might kill either nutrient, normal or tumor cells. Using a wide spectrum of parameters we examined survival of our species and tried to identify the corresponding dynamical regimes. It was found that the radiotherapy influence…
Semiempirical pseudopotential approach for nitride-based nanostructures and {\it ab initio} based passivation of free surfaces
2013
We present a semiempirical pseudopotential method based on screened atomic pseudopotentials and derived from \textit{ab initio} calculations. This approach is motivated by the demand for pseudopotentials able to address nanostructures, where \textit{ab initio} methods are both too costly and insufficiently accurate at the level of the local-density approximation, while mesoscopic effective-mass approaches are inapplicable due to the small size of the structures along, at least, one dimension. In this work we improve the traditional pseudopotential method by a two-step process: First, we invert a set of self-consistently determined screened {\it ab initio} potentials in wurtzite GaN for a ra…