Showing papers by "Margaret H. Wright published in 1980"
TL;DR: Some aspects of modelling that influence the performance of optimization methods are discussed, including the construction of smooth models, the transformation of an optimization problem from one category to another, scaling, formulation of constraints, and techniques for special types of models.
16 citations
01 May 1980
TL;DR: Methods for estimating the relative cancellation error and relative truncation error in a finite-difference approximation are discussed and a technique for computing the finite-Difference interval so that the bounds upon the errors are balanced is proposed.
Abstract: : Finite-difference approximations to derivatives are useful not only in optimization algorithms, but also in other circumstances such as sensitivity analysis. In this paper we discuss methods for estimating the relative cancellation error and relative truncation error in a finite-difference approximation and propose a technique for computing the finite-difference interval so that the bounds upon the errors are balanced. We also propose a method for choosing the finite-difference interval in a quasi-Newton algorithm for unconstrained minimization that uses function values only. (Author)
14 citations
01 Oct 1980
TL;DR: In this paper, a variant of the ellipsoid update is developed, to take advantage of the range constraints that often occur in linear programs (i.e., constraints of the form l or = aTx or = u, where u - l is reasonably small).
Abstract: : The ellipsoid algorithm associated with Shor, Khachiyan and others has certain theoretical properties that suggest its use as a linear programming algorithm. Some of the practical difficulties are investigated here. A variant of the ellipsoid update is first developed, to take advantage of the range constraints that often occur in linear programs (i.e., constraints of the form l or = aTx or = u, where u - l is reasonably small). Methods for storing the ellipsoid matrix are then discussed for both dense and sparse problems. In the large-scale case, a major difficulty is that the desired ellipsoid cannot be represented compactly throughout an arbitrary number of iterations. Some schemes are suggested for economizing on storage, but any guarantee of convergence is effectively lost. At this stage there remains little room for optimism that an ellipsoid-based algorithm could complete with the simplex method on problems with a large number of variables. (Author)
6 citations
01 May 1980
TL;DR: A brief survey of the state of the art of numerical optimization is presented, in which those methods that are directly applicable to power system problems will be highlighted.
Abstract: : The application of optimization to electrical power technology often requires the numerical solution of systems that are very large and possibly non-differentiable. A brief survey of the state of the art of numerical optimization is presented in which those methods that are directly applicable to power system problems will be highlighted. The areas of current research that are most likely to yield direct benefit to practical computation are identified. The paper concludes with a survey of available software. (Author)
3 citations