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...

Inequality constraints are often needed in optimization problems in order to deal with uncertainty. This paper introduces a simple technique that allows enforcement of inequality constraints in `1 norm problems without any modi cations to existing programs. The solution of `1 norm problems is required, for example, in implementing LAV (Least Absolute Value) state estimators in electric power sy...

Since the late 1990s, the interest in augmented Lagrangian methods has been revived, and several models with smooth penalty functions for programs with inequality constraints have been proposed, tested and used in a variety of applications. Global convergence results for some of these methods have been published. Here we present a local convergence analysis for a large class of smooth augmented...

In many practical applications, the need arises to aggregate data of varying dimension. Following from the self-identity property, some recent studies have looked at the stability of aggregation operators in terms of their behavior as the dimensionality is increased from n−1 to n. We use the penalty-based representation of aggregation functions in order to investigate the conditions for weighti...

We study the problem of learning a sparse linear regression vector under additional conditions on the structure of its sparsity pattern. This problem is relevant in Machine Learning, Statistics and Signal Processing. It is well known that a linear regression can benefit from knowledge that the underlying regression vector is sparse. The combinatorial problem of selecting the nonzero components ...

[Received on 31 March 2007] We propose a globalization strategy for nonlinear constrained optimization. The method employs a “flexible” penalty function to promote convergence, where during each iteration the penalty parameter can be chosen as any number within a prescribed interval, rather than a fixed value. This increased flexibility in the step acceptance procedure is designed to promote lo...

Given an undirected graph G = (V,E), a graph orientation problem is to decide a direction for each edge so that the resulting directed graph G⃗ = (V,Λ(E)) satisfies a certain condition, where Λ(E) is a set of assignments of a direction to each edge {u, v} ∈ E. Among many conceivable types of conditions, we consider a degree constrained orientation: Given positive integers av and bv for each v (a...