1,922 research outputs found
Adaptive Regularization for Nonconvex Optimization Using Inexact Function Values and Randomly Perturbed Derivatives
A regularization algorithm allowing random noise in derivatives and inexact
function values is proposed for computing approximate local critical points of
any order for smooth unconstrained optimization problems. For an objective
function with Lipschitz continuous -th derivative and given an arbitrary
optimality order , it is shown that this algorithm will, in
expectation, compute such a point in at most
inexact evaluations of and its derivatives whenever , where
is the tolerance for th order accuracy. This bound becomes at
most
inexact evaluations if and all derivatives are Lipschitz continuous.
Moreover these bounds are sharp in the order of the accuracy tolerances. An
extension to convexly constrained problems is also outlined.Comment: 22 page
Adaptive Regularization Algorithms with Inexact Evaluations for Nonconvex Optimization
A regularization algorithm using inexact function values and inexact
derivatives is proposed and its evaluation complexity analyzed. This algorithm
is applicable to unconstrained problems and to problems with inexpensive
constraints (that is constraints whose evaluation and enforcement has
negligible cost) under the assumption that the derivative of highest degree is
-H\"{o}lder continuous. It features a very flexible adaptive mechanism
for determining the inexactness which is allowed, at each iteration, when
computing objective function values and derivatives. The complexity analysis
covers arbitrary optimality order and arbitrary degree of available approximate
derivatives. It extends results of Cartis, Gould and Toint (2018) on the
evaluation complexity to the inexact case: if a th order minimizer is sought
using approximations to the first derivatives, it is proved that a suitable
approximate minimizer within is computed by the proposed algorithm
in at most iterations and at most
approximate
evaluations. An algorithmic variant, although more rigid in practice, can be
proved to find such an approximate minimizer in
evaluations.While
the proposed framework remains so far conceptual for high degrees and orders,
it is shown to yield simple and computationally realistic inexact methods when
specialized to the unconstrained and bound-constrained first- and second-order
cases. The deterministic complexity results are finally extended to the
stochastic context, yielding adaptive sample-size rules for subsampling methods
typical of machine learning.Comment: 32 page
Sleeping with the enemy. The not-so-constant Italian stance towards Russia
A taken-for-granted assumption within the Italian foreign affairs community argues that the relationship between
Rome and Moscow follows a generally cooperative attitude, fostered by strong cultural, economic and political
ties. This narrative misses a significant part of the tale, which is at odds with the idea that the good relations with
Russia are a ‘constant feature’ of Italy’s foreign policy. Indeed, competitive interaction has frequently emerged,
as a number of events in the last decade confirm. To challenge conventional wisdom, the article aims to provide
a more nuanced interpretation of the investigated relationship. Focusing on the outcomes of global structural
changes on Italian foreign policy, it posits that Rome is more prone to a cooperative stance towards Moscow
whenever the international order proves stable. By contrast, its interests gradually diverge from those of its alleged
‘natural’ partner as the international order becomes increasingly unstable. This hypothesis is tested by an
in-depth analysis of Italy’s posture towards Russia amidst the crisis of the international liberal order (2008-on).
Furthermore, the recurrence of a similar dynamic is verified through a diachronic comparison with two other
international orders in crisis, i.e. that of the interwar period (1936-1941) and that of the Cold War (1979-1985)
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Experimental and Numerical Analysis of Single Phase Flow in a micro T-junction
This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.In this work the fluid-dynamic behaviour of a micro T-junction has been investigated both
numerically and experimentally for low Reynolds numbers (Re<14) with water as working fluid. The
velocity profiles within the T-junction has been experimentally determined by using the micro Particle Image
Velocimetry (μPIV). The experimental data have been compared with the numerical results obtained by
means of a 3D model implemented in Comsol Multiphysics® environment for incompressible, isothermal,
laminar flows with constant properties. The comparison between the experimental and the numerical data
puts in evidence a perfect agreement among the results. In the central region of the T-junction where the
velocity profiles of the inlet branches interact, the maximum difference is less than 5.8% for different flow
rates imposed at the inlet (with the ratio 1:2) and less than 4.4% in the case of the same flow rate at the inlets
(1:1). Since the estimated uncertainty of the experimental velocity is about 3%, the obtained result can be
considered very good and it demonstrates that no significant scaling effects influences the liquid mixing for
low Reynolds numbers (Re<14) and the behaviour of the micro T-junction can be considered as
conventional. The detailed analysis of the velocity profile evolution within the central region of the mixer
has allowed to determine where the fully developed laminar profile is reached (for instance 260 mm far from
the centre of the T-junction when a maximum water flow rate of 8 ml/h is considered)
Dynamic energy release rate in couple-stress elasticity
This paper is concerned with energy release rate for dynamic steady state crack problems in elastic materials with microstructures. A Mode III semi-infinite crack subject to loading applied on the crack surfaces is considered. The micropolar behaviour of the material is described by the theory of couple-stress elasticity developed by Koiter. A general expression for the dynamic J-integral including both traslational and micro-rotational inertial contributions is derived, and the conservation of this integral on a path surrounding the crack tip is demonstrated
Remarks on the energy release rate for an antiplane moving crack in couple stress elasticity
This paper is concerned with the steady-state propagation of an antiplane
semi-infinite crack in couple stress elastic materials. A distributed loading
applied at the crack faces and moving with the same velocity of the crack tip
is considered, and the influence of the loading profile variations and
microstructural effects on the dynamic energy release rate is investigated. The
behaviour of both energy release rate and maximum total shear stress when the
crack tip speed approaches the critical speed (either that of the shear waves
or that of the localised surface waves) is studied. The limit case
corresponding to vanishing characteristic scale lengths is addressed both
numerically and analytically by means of a comparison with classical elasticity
results.Comment: 37 pages, 13 figure
A Non-Local Mean Curvature Flow and its semi-implicit time-discrete approximation
We address in this paper the study of a geometric evolution, corresponding to
a curvature which is non-local and singular at the origin. The curvature
represents the first variation of the energy recently proposed as a variant of
the standard perimeter penalization for the denoising of nonsmooth curves.
To deal with such degeneracies, we first give an abstract existence and
uniqueness result for viscosity solutions of non-local degenerate Hamiltonians,
satisfying suitable continuity assumption with respect to Kuratowsky
convergence of the level sets. This abstract setting applies to an approximated
flow. Then, by the method of minimizing movements, we also build an "exact"
curvature flow, and we illustrate some examples, comparing the results with the
standard mean curvature flow
The strange case of negative reflection
In this paper, we show the phenomenon of negative reflection occurring in a mechanical phononic structure, consisting of a grating of fixed inclusions embedded in a linear elastic matrix. The negative reflection is not due to the introduction of a subwavelength metastructure or materials with negative mechanical properties. Numerical analyses for out-of-plane shear waves demonstrate that there exist frequencies at which most of the incident energy is reflected at negative angles. The effect is symmetric with respect to a line that is not parallel to the normal direction to the grating structure. Simulations at different angles of incidence and computations of the energy fluxes show that negative reflection is achievable in a wide range of loading conditions
Integral identities for a semi-infinite interfacial crack in anisotropic elastic bimaterials
The focus of the article is on the analysis of a semi-infinite crack at the
interface between two dissimilar anisotropic elastic materials, loaded by a
general asymmetrical system of forces acting on the crack faces. Recently
derived symmetric and skew-symmetric weight function matrices are introduced
for both plane strain and antiplane shear cracks, and used together with the
fundamental reciprocal identity (Betti formula) in order to formulate the
elastic fracture problem in terms of singular integral equations relating the
applied loading and the resulting crack opening. The proposed compact
formulation can be used to solve many problems in linear elastic fracture
mechanics (for example various classic crack problems in homogeneous and
heterogeneous anisotropic media, as piezoceramics or composite materials). This
formulation is also fundamental in many multifield theories, where the elastic
problem is coupled with other concurrent physical phenomena.Comment: 29 pages, 4 figure
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