5,827 research outputs found
Local Convergence of the Affine-Scaling Interior-Point Algorithm for Nonlinear Programming
This paper addresses the local convergence properties of the affine-scaling interior-point algorithm for nonlinear programming. The analysis of local convergence is developed in terms of parameters that control the interior-point scheme and the size of the residual of the linear system that provides the step direction. The analysis follows the classical theory for quasi-Newton methods and addresses q-linear, q-superlinear, and q-quadratic rates of convergence
Implicitly and densely discrete black-box optimization problems
This paper addresses derivative-free optimization problems where the
variables lie implicitly in an unknown discrete closed set. The evaluation of the
objective function follows a projection onto the discrete set, which is assumed dense
rather than sparse. Such a mathematical setting is a rough representation of what
is common in many real-life applications where, despite the continuous nature of
the underlying models, a number of practical issues dictate rounding of values or
projection to nearby feasible figures.
We discuss a definition of minimization for these implicitly discrete problems and
outline a direct search algorithm framework for its solution. The main asymptotic
properties of the algorithm are analyzed and numerically illustrated.FCT POCI/MAT/59442/2004, PTDC/MAT/64838/200
Implicitly and densely discrete black-box optimization problems
This paper addresses derivative-free optimization problems where the
variables lie implicitly in an unknown discrete closed set. The evaluation of the
objective function follows a projection onto the discrete set, which is assumed dense
rather than sparse. Such a mathematical setting is a rough representation of what
is common in many real-life applications where, despite the continuous nature of
the underlying models, a number of practical issues dictate rounding of values or
projection to nearby feasible figures.
We discuss a definition of minimization for these implicitly discrete problems and
outline a direct search algorithm framework for its solution. The main asymptotic
properties of the algorithm are analyzed and numerically illustrated.FCT POCI/MAT/59442/2004, PTDC/MAT/64838/200
Estimation of Risk-Neutral Density Surfaces
Option price data is often used to infer risk-neutral densities for future prices of an underlying asset. Given the prices of a set of options on the same underlying asset with different strikes and maturities, we propose a nonparametric approach for estimating risk-neutral densities associated with several maturities. Our method uses bicubic splines in order to achieve the desired smoothness for the estimation and an optimization model to choose the spline functions that best fit the price data. Semidefinite programming is employed to guarantee the nonnegativity of the densities. We illustrate the process using synthetic option price data generated using log-normal and absolute diffusion processes as well as actual price data for options on the S&P500 index. We also used the risk-neutral densities that we computed to price exotic options and observed that this approach generates prices that closely approximate the market prices of these options.
Tilt Induced Localization and Delocalization in the Second Landau Level
We have investigated the behavior of electronic phases of the second Landau
level under tilted magnetic fields. The fractional quantum Hall liquids at
2+1/5 and 2+4/5 and the solid phases at 2.30, 2.44, 2.57, and 2.70
are quickly destroyed with tilt. This behavior can be interpreted as a tilt
driven localization of the 2+1/5 and 2+4/5 fractional quantum Hall liquids and
a delocalization through melting of solid phases in the top Landau level,
respectively. The evolution towards the classical Hall gas of the solid phases
is suggestive of antiferromagnetic ordering
Large scale structure simulations of inhomogeneous LTB void models
We perform numerical simulations of large scale structure evolution in an
inhomogeneous Lemaitre-Tolman-Bondi (LTB) model of the Universe. We follow the
gravitational collapse of a large underdense region (a void) in an otherwise
flat matter-dominated Einstein-deSitter model. We observe how the (background)
density contrast at the centre of the void grows to be of order one, and show
that the density and velocity profiles follow the exact non-linear LTB solution
to the full Einstein equations for all but the most extreme voids. This result
seems to contradict previous claims that fully relativistic codes are needed to
properly handle the non-linear evolution of large scale structures, and that
local Newtonian dynamics with an explicit expansion term is not adequate. We
also find that the (local) matter density contrast grows with the scale factor
in a way analogous to that of an open universe with a value of the matter
density OmegaM(r) corresponding to the appropriate location within the void.Comment: 7 pages, 6 figures, published in Physical Review
Quantization of the diagonal resistance: Density gradients and the empirical resistance rule in a 2D system
We have observed quantization of the diagonal resistance, R_xx, at the edges
of several quantum Hall states. Each quantized R_xx value is close to the
difference between the two adjacent Hall plateaus in the off-diagonal
resistance, R_xy. Peaks in R_xx occur at different positions in positive and
negative magnetic fields. Practically all R_xx features can be explained
quantitatively by a ~1%/cm electron density gradient. Therefore, R_xx is
determined by R_xy and unrelated to the diagonal resistivity rho_xx. Our
findings throw an unexpected light on the empirical resistivity rule for 2D
systems
Myomectomy in Early Pregnancy - A Case Report
Uterine leiomyomas are by far the most
common benign tumours of the female genital tract. The true incidence of leiomyomas during pregnancy is, however, unknown. Although leiomyomas usually remain
asymptomatic during pregnancy, they may complicate its course. The management of leiomyoma during pregnancy is medical, but, in rare circumstances, surgical intervention
and myomectomy may be required. A case of myomectomy in early pregnancy is described
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