|Treating constrained problems with EAs is a big challange to the eld. Whether one considers constrained optmization problems or constraint satisfaction problems, the presence of a tness function (penalty function) reeect-ing consraint violation is essential. The deenition of such a penalty function has a great impact on the GA performance , and it is therefore very important to chose it proper...

We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. We present a family of convex penalty functions, which encode this prior knowledge by means of a set of constraints on the absolute values of the regression coefficients. This family subsumes the l1 norm and is flexible enough to include different models of sp...

We propose a method for solving nonlinear second-order cone programs (SOCPs), based on a continuously differentiable exact penalty function. The construction of the penalty function is given by incorporating a multipliers estimate in the augmented Lagrangian for SOCPs. Under the nondegeneracy assumption and the strong second-order sufficient condition, we show that a generalized Newton method h...

Reduction of number of image colors is an important task for presentation, transmission, segmentation, and compression of color images. In most cases, it is easier to process and understand an image with a limited number of colors. Color image reduction speeds up the manipulations on an image and reduces the storage cost and transmission cost. Various techniques have been proposed for color ima...

This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functio...

We consider, for the first time, general diminishing stepsize methods for nonconvex, constrained optimization problems. We show that by using directions obtained in an SQP-like fashion convergence to generalized stationary points can be proved. In order to do so, we make use of classical penalty functions in an unconventional way. In particular, penalty functions only enter in the theoretical a...

1. Abstract A well-known approach for solving constrained optimization problems is based on penalty functions. A penalty technique transforms the constrained problem into an unconstrained problem by penalizing the objective function when constraints are violated and then minimizing the penalty function using methods for unconstrained problems. In this paper, we analyze the implementation of a s...

This paper analyzes situations in which a project consisting of several activities is not realized according to plan. If the project is expedited, a reward arises. Analogously, a penalty arises if the project is delayed. This paper considers the case of arbitrary nondecreasing reward and penalty functions on the total expedition and delay, respectively. Attention is focused on how to divide the...

In this work we study the relation between restricted dissimilarity functions-and, more generally, dissimilarity-like functionsand penalty functions and the possibility of building the latter using the former. Several results on convexity and quasiconvexity are also considered.

Kalyanmoy Deb and Samir Agrawal Kanpur Genetic Algorithms Laboratory (KanGAL), Department of Mechanical Engineering, Indian Institute of Technology Kanpur, PIN 208 016, India E-mail: deb,samira @iitk.ac.in Abstract Most applications of genetic algorithms (GAs) in handling constraints use a straightforward penalty function method. Such techniques involve penalty parameters which must be set righ...