Support vector machine (SVM) is an important and fundamental technique in learning. Soft-margin SVM models have stronger generalization performance compared with the hard-margin SVM. Most existing works use hinge-loss function which can be regarded as upper bound of 0–1 loss function. However, it cannot explicitly control number misclassified samples. In this paper, we idea soft-margin propose ...

A Posteriori Error Analysis in the maximum norm for a penalty finite element method for the time-dependent obstacle problem Abstract. We consider nite element approximation of the parabolic obstacle problem. The analysis is based on a penalty formulation of the problem where the penalisation parameter is allowed to vary in space and time. We estimate the penalisation error in terms of the penal...

We use a primal-dual scheme to devise a new update rule for a penalty function method applicable to general optimization problems, including nonsmooth and nonconvex ones. The update rule we introduce uses dual information in a simple way. Numerical test problems show that our update rule has certain advantages over the classical one. We study the relationship between exact penalty parameters an...

Survey research finds that mothers suffer a substantial per-child wage penalty that is not explained by human capital or occupational factors (Budig and England 2001; Anderson, Binder and Krause 2003). Despite clear documentation of this pattern, the causal mechanism producing it remains elusive because existing research has not been able to distinguish between productivity and discrimination e...

This paper presents an abstract analysis of bounded variation (BY) methods for illposed apentor equations Au = L. Let where the penalty, or 'regularization'. parameter (I > 0 and the functional J ( u ) is the BY norm or semi-norm of U , also known 3s the total variation of U. Under mild restrictions on the operator A and the functional J ( u ) , it is shown that the functional T ( u ) has a uni...

The finite mixture of normal distributions in both mean and variance parameters have wide applications. It is well known that the likelihood function of this model is unbounded for any given sample size. Hence, the ordinary maximum likelihood estimator is not consistent. At the same time, a local maximum of the likelihood function can often be found to have good statistical properties. In this ...

We consider dynamical and quasi-static thermoelastic contact problems in R modeling the evolution of temperature and displacement in an elastic body that may come into contact with a rigid foundation. The existence of solutions to these dynamical and quasi-static nonlinear problems and the exponential stability are investigated using a penalty method. Interior smoothing effects in the quasi-sta...