We provide a simple and efficient algorithm for the projection operator for weighted l1-norm regularization subject to a sum constraint, together with an elementary proof. The implementation of the proposed algorithm can be downloaded from the author’s homepage. 1 The problem In this report, we consider the following optimization problem: min x 1 2 ‖x − y‖ 2 + n

Quantum gravity is made more difficult in part by its constraint structure. The constraints are classically first-class; however, upon quantization they become partially second-class. To study such behavior, we focus on a simple problem with finitely many degrees of freedom and demonstrate how the projection operator formalism for dealing with quantum constraints is well suited to this type of ...

We provide a simple and efficient algorithm for the projection operator for weighted l1-norm regularization subject to a sum constraint, together with an elementary proof. The implementation of the proposed algorithm can be downloaded from the author’s homepage. 1 The problem In this report, we consider the following optimization problem: min x 1 2 ‖x− y‖ 2 + n

We present an efficient spectral projected-gradient algorithm for optimization subject to a group `1-norm constraint. Our approach is based on a novel linear-time algorithm for Euclidean projection onto the `1and group `1-norm constraints. Numerical experiments on large data sets suggest that the proposed method is substantially more efficient and scalable than existing methods.

A new technique for designing digital allpass IIR filters is proposed. The approach is based on the vector space projection method. Constraint sets, and their associated projectors, that capture the properties of the desired group delay are given. Examples that demonstrate the advantages and flexibility of this method as well as comparisons with a wellknown method are furnished

In the standard framework of data envelopment analysis (DEA) models, the returns to scale are fully characterized using the multiplier on the convexity constraint of inefficient decision making units (DMU) using the projection of the input-output vector on the frontier. In this note, we investigate how the returns to scale measurements in DEA models are affected by the presence of regulatory co...

Ventricular constraint therapy has been used to prevent and reverse the progression of heart failure in ischemic and nonischemic cardiomyopathies. We hypothesized that ventricular restraint should be tried by closing the pericardium that was previously opened following left ventricle topographical projection. The surgical technique presentation is illustrated by a remarkable 13-year outcome of ...

Quadratic constraints on the weight vector of an adaptive linearly constrained minimum power (LCMP) beamformer can improve robustness to pointing errors and to random perturbations in sensor parameters. In this paper, we propose a technique for implementing a quadratic inequality constraint with recursive least squares (RLS) updating. A variable diagonal loading term is added at each step, wher...

The nonlinear matrix equation X+A∗X−1A = Q can be cast as a linear Sylvester equation subject to unitary constraint. The Sylvester equation can be obtained by means of hermitian eigenvalue computation. The unitary constraint can be satisfied by means of either a straightforward alternating projection method or by a coordinate-free Newton iteration. The idea proposed in this paper originates fro...

In the previous work, we have developed a method for visual imitation by recovering the demonstrator’s view based on the stereo epipolar constraint [1]. The method is applied to the stationary pair of the stereo cameras, therefore, the visual fields to observe the both motions of the demonstrator and the learner are limited. This paper presents a method to extend our previous work by adopting a...