Piecewise Linear-Quadratic (PLQ) penalties are widely used to develop models in statistical inference, signal processing, and machine learning. Common examples of PLQ include least squares, Huber, Vapnik, 1-norm, their asymmetric generalizations. Properties these estimators depend on the choice penalty its shape parameters, such as degree asymmetry for quantile loss, transition point between li...

The classical Taguchi quality model only considers the control of quality. Huang[9] proposed a model that took both quality and cost into account. Huang’s model presents a trade-off problem between quality and cost, in which higher quality is not the final aim but the profit. In Huang’s model, the symmetrical quadratic quality loss function was employed to stand for the loss of profit. In this ...

BACKGROUND Understanding the quality loss implications of short staffing is essential in maintaining service quality on a limited budget. OBJECTIVES For elaborate financial control on staffing decisions, it is necessary to quantify the cost of the incidental quality loss that a given workload and staffing level entail. DESIGN We develop a quantitative methodology that uses a quality loss fu...

Estimators of the reliability function in a GLM (generalized life model) are considered. The class of the GLM includes (among others) the Weibull, Pareto, Beta, Gompertz, and Rayleigh distribution. A proper general prior density and the predictive function for general class of distribution proposed by Al-Hussaini [1] are used to obtain the exact estimate. Also, the Bayes estimates relative to s...

multi objective quadratic fractional programming (moqfp) problem involves optimization of several objective functions in the form of a ratio of numerator and denominator functions which involve both contains linear and quadratic forms with the assumption that the set of feasible solutions is a convex polyhedral with a nite number of extreme points and the denominator part of each of the object...

the study of stability problems of functional equations was motivated by a question of s.m. ulam asked in 1940. the first result giving answer to this question is due to d.h. hyers. subsequently, his result was extended and generalized in several ways.we prove some hyperstability results for the equation g(ax+by)+g(cx+dy)=ag(x)+bg(y)on restricted domain. namely, we show, under some weak natural...

the energy loss of a 3-dimensional harmonic oscillator due to the quadrupole radiation in quadratic f (r) gravity is calculated.

The support vector regression (SVR) model is usually fitted by solving a quadratic programming problem, which is computationally expensive. To improve the computational efficiency, we propose to directly minimize the objective function in the primal form. However, the loss function used by SVR is not differentiable, which prevents the well-developed gradient based optimization methods from bein...