This article compares three penalty terms with respect to the efficiency of supervised learning, by using first- and second-order off-line learning algorithms and a first-order on-line algorithm. Our experiments showed that for a reasonably adequate penalty factor, the combination of the squared penalty term and the second-order learning algorithm drastically improves the convergence performanc...

This section begins with the motivation and general form of penalty functions as used in evolutionary computation. The main types of penalty function—constant, static, dynamic, and adaptive—are described within a common notation framework. References from the literature concerning these exterior penalty approaches are presented. The section concludes with a brief discussion of promising areas o...

Exact penalty approach aims at replacing a constrained optimization problem by an equivalent unconstrained optimization problem. Most of results in the literature of exact penalization are mainly concerned with finding conditions under which a solution of the constrained optimization problem is a solution of an unconstrained penalized optimization problem and the reverse property is rarely stud...

Exact penalty methods for the solution of constrained optimization problems are based on the construction of a function whose unconstrained minimizing points are also solution of the constrained problem. In the rst part of this paper we recall some deenitions concerning exactness properties of penalty functions, of barrier functions, of augmented Lagrangian functions, and discuss under which as...

A drawback of the sparse principal component analysis (PCA) procedures using penalty functions is that the number of zeros in the matrix of component loadings as a whole cannot be specified in advance. We thus propose a new sparse PCA procedure in which the least squares PCA loss function is minimized subject to a pre-specified number of zeros in the loading matrix. The procedure is called unpe...

S countries abolish the death penalty during their transition from war to peace or from an authoritarian to a democratic regime. In other cases, countries regard the death penalty as a necessary policy to promote their transition. In whatever way, it seems that the transition process has some impact on death penalty policy. How and to what extent is this so, and what exactly are the elements th...

We have compared the performance of two different penalty choices for a penalized-likelihood sinogram-restoration strategy we have been developing. One is a quadratic penalty we have employed previously and the other is a new median-based penalty. We compared the approaches to a noniterative adaptive filter that loosely but not explicitly models data statistics. We found that the two approaches...

Likelihood-based estimators with conventional regularization methods generally produces images with nonuniform and anisotropic spatial resolution properties. Previous work on penalty design for penalizedlikelihood estimators has led to statistical reconstruction methods that yield approximately uniform “average” resolution. However some asymmetries in the local point-spread functions persist. S...

In this paper, we present an algorithm to solve the inequality constrained multi-objective programming (MP) by using a penalty function with objective parameters and constraint penalty parameter. First, the penalty function with objective parameters and constraint penalty parameter for MP and the corresponding unconstraint penalty optimization problem (UPOP) is defined. Under some conditions, a...

In this paper we introduce a modified penalty function (MPF) method for solving a problem which minimizes a nonlinear programming subject to inequality constraints. Basically, this method is a combination of the modified penalty methods and the Lagrangian methods. It treats inequality constraints with a modified penalty function and avoids the indifferentiability of max {x, 0}. This method alte...