Given a time series of observed positions {ri} N i=0 objective is to generate a smooth trajectory to fit these data points. in three dimensional space, our primary A penalty term is introduced to assure smoothness of the reconstructed trajectory. N∑ ‖r(ti) − ri ‖ 2

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In the context of a Brownian filtration and with a fixed finite time horizon, we will provide a representation of the penalty term of general dynamic concave utilities (hence of dynamic convex risk measures) by applying the theory of g-expectations. 1

This paper compares three penalty terms with respect to the efficiency of supervised learning, by using first- and second-order learning algorithms. Our experiments showed that for a reasonably adequate penalty factor, the combination of the squared penalty term and the second-order learning

Nonrigid registration of medical images usually does not model properties of different tissue types. This results for example in nonrigid deformations of structures that are rigid. In this work we address this problem by employ-ing a local rigidity penalty term. We illustrate this approach on a 2D

Robust utility maximization with an entropic penalty term: Stochastic control and BSDE methods

We consider the stable approximation of sparse solutions to non-linear operator equations by means of Tikhonov regularization with a subquadratic penalty term. Imposing certain assumptions, which for a linear operator are equivalent to the standard range condition, we derive the usual convergence

. Iterative methods are considered for a class of saddle point problems with a penalty term arising from finite element discretizations of certain elliptic problems. An optimal preconditioner which is independent of the discretization and the penalty parameter is constructed. This approach

Abstract—Detection of the number of sinusoids embedded in noise is a fundamental problem in statistical signal processing. Most parametric methods minimize the sum of a data fit (likelihood) term and a complexity penalty term. The latter is often derived via information theoretic criteria

of an appropriately defined objective function. The objective function can be separated into a least-square-error term, which compares predicted and actual detector readings, and additional penalty terms that may contain a priori information about the system. For the efficient minimization of this objective function