Michael W. Leonard

Learn More
Limited-memory BFGS quasi-Newton methods approximate the Hessian matrix of second derivatives by the sum of a diagonal matrix and a fixed number of rank-one matrices. These methods are particularly effective for large problems in which the approximate Hessian cannot be stored explicitly. It can be shown that the conventional BFGS method accumulates(More)
We propose a sequential quadratic programming (SQP) method for the optimal control of large-scale dynamical systems. The method uses modified multiple shooting to discretize the dynamical constraints. When these systems have relatively few parameters, the computational complexity of the modified method is much less than that of standard multiple shooting.(More)
The molecular mechanisms specifying patterns of gene expression in the vertebrate brain, which in turn determine the developmental fates of specific neurons, are yet to be clearly defined. Individual members of a recently identified family of transcriptional regulatory proteins, the GATA factors, are required for the differentiation of certain hematopoietic(More)
Quasi-Newton methods are reliable and eecient on a wide range of problems, but they can require many iterations if no good estimate of the Hessian is available or the problem is ill-conditioned. Methods that are less susceptible to ill-conditioning can be formulated by exploiting the fact that quasi-Newton methods accumulate second-derivative information in(More)
Singular spectrum analysis (SSA) is a relatively new approach to modeling time series data. Now supported in SAS/ETS software, the SSA method of time series analysis applies nonparametric techniques to decompose time series into principal components. SSA is particularly valuable for long time series, for which patterns (such as trends and cycles) are(More)
Many businesses use sales promotions to increase the demand for or visibility of a product or service. These promotions often require increased expenditures (such as advertising) or loss of revenue (such as discounts), and/or additional costs (such as increased production). Business leaders need to determine the value of previous or proposed promotions. One(More)
PURPOSE This study was undertaken to evaluate the efficacy of a proximal humeral locking plate, and to specifically study the effect of patient age and fracture type on the outcome. MATERIALS AND METHODS Thirty-one cases of proximal humeral fractures fixed by using the proximal humeral interlocking (PHILOS) plate were reviewed. RESULTS Average(More)