A generalized direct search acceptable-point technique for use with descent-type multivariate algorithms

Many non-linear programming algorithms employ a univariate subprocedure to determine the step length at each multivariate iteration. In recent years much work has been directed toward the development of algorithms which will exhibit favorable convergence properties on well-behaved functions without requiring that the univariate algorithm perform a sequence of one-dimensional minimizations.In this paper a direct search method (the golden section search) is modified to search for acceptable rather than minimizing step lengths and then used as the univariate subprocedure for a generalized conjugate gradient algorithm. The resulting multivariate minimization method is tested on standard unconstrained test functions and a constrained industrial problem. The new method is found to be relatively insensitive to tuning parameters (insofar as success or failure is concerned).A comparison of the golden section acceptable-point search (GSAP) with other popular acceptable-point methods indicates that GSAP is a superior strategy for use with the conjugate directions-type algorithms and is also suitable for use with the quasi-Newton methods. The comparison are based on equivalent function evaluations required to minimize multivariate test functions.     

Special functions of circuits and systems

The polynomial solutions of the equation fy″ + gy′ + λy = 0 are obtained and classified for f, g, and λ certain second-degree, first-degree, and zero-degree polynomials, respectively. Applications are given illustrating the use of these polynomials in the construction of amplitude functions and system functions and in tree counting. In particular, all-pole and rational filter functions are considered which include as special cases the Chebyshev, Butterworth, elliptic, Bessel, and various transitional filter functions.     

Our House on Mango Street

We didn＇t always live on Mango Street. Before that we lived on Loomis on the third floor, and before that we lived on Keeler. Before Keeler it was Paulina, and before that I can＇t remember. But what I remember most is moving a lot. Each time it seemed there＇d be one more of us. By the time we got to Mango Street we were six--Mama, Papa, Carlos, Kiki, my sister Nenny and me.     

Discovering patterns in interarrival data

It is suggested that students collect interarrival data for customers arriving at a queue. Two common features will often occur across these various datasets. Some data collection hints, some problems for students to pursue and a few pointers to the literature are given.