Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control over the desired level of sparsity of estimators. We analyze its structural properties and in doing so show the following: 1. Drawing parallels between robus...

Tax identities and discounted penalty functions in collective risk theory

When aligning biological sequences, the choice of parameter values for the alignment scoring function is critical. Small changes in gap penalties, for example, can yield radically different alignments. A rigorous way to compute parameter values that are appropriate for biological sequences is inverse parametric sequence alignment. Given a collection of examples of biologically correct alignment...

EQUALITY CONSTRAINED OPTIMIZATION Masao Fukushima Kyoto University Hisashi Mine Kansai University Eiki Yamakawa Kyoto University (Received November 12, 1984: Revised June 12, 1985) This paper is concerned with a differentiable exact penalty function derived by modifying the Wolfe dual of an equality constrained problem. It may be considered that this penalty function belongs to a class of gener...

Optimum design of structures is achieved while the design variables are continuous and discrete. To reduce the computational work involved in the optimization process, all the functions that are expensive to evaluate, are approximated. To approximate these functions, a semi quadratic function is employed. Only the diagonal terms of the Hessian matrix are used and these elements are estimated fr...

In this paper we present an integration of optirnisation, priority setting, planning and combining of maintenance activities. We use a framework which covers several optimisation models, like the block replacement, a minimal repair and an efficiency model, and develop a uniform analysis for all these models. From this analysis penalty functions are derived which can act as priority criterion fu...

This article studies a large class of averaging aggregation functions based on minimizing a distance from the vector of inputs, or equivalently, minimizing a penalty imposed for deviations of individual inputs from the aggregated value. We provide a systematization of various ty es of penalty based aggregation functions, and show how many special cases arise as the result. We show how new aggre...

Ill-conditioned inverse problems are often encountered in signal/image processing. In this respect, convex objective functions including a sparsity promoting penalty term can be used. However, most of the existing optimization algorithms were developed for real-valued signals. In this paper, we are interested in complex-valued data. More precisely, we consider a class of penalty functions for w...

This paper presents a novel bi-objective manpower scheduling problem that minimizes the penalty resulted from employees’ assignment at lower skill levels than their real skill and maximizes employees’ utility for working at a special skill level in some shifts or on some days. Employees are classified in two specialist groups and three skill levels in each specialization. In addition, the prese...