A Generalized Computer Technique for Solving Unconstrained Non-Linear Programming Problems

An unconstrained problem with nonlinear objective function has many applications. This is often viewed as a discipline in and of itself. In this paper, we develop a computer technique for solving nonlinear unconstrained problems in a single framework incorporating with Golden section, Gradient Search method. For this, we first combine this algorithm and then develop a generalized computer technique using the programming language MATHEMATICA. We demonstrate our computer technique with a number of numerical examples. Dhaka Univ. J. Sci. 61(1): 75-80, 2013 (January) DOI: http://dx.doi.org/10.3329/dujs.v61i1.15100

SEMICLASSICAL FORMULATION OF OPTIMAL CONTROL THEORY

In the present paper, semiclassical formulation of optimal control theory is made by combining the conjugate gradient search method with new approximate semiclassical expressions for correlation function. Two expressions for correlation function are derived. The simpler one requires calculations of coordinates and momenta of classical trajectories only. The second one requires extra calculation of common semiclassical quantities; as a result additional quantum effects can be taken into account. The efficiency of the method is demonstrated by controlling nuclear wave packet motion in a two-dimensional model system.

Design Optimization of Valveless DTH Pneumatic Hammers by a Weighted Pseudo-Gradient Search Method

A design methodology for Down-The-Hole (DTH) pneumatic hammers used for rock drilling is proposed which renders an optimal design for a given set of constraints. A generic non-linear dynamic model developed by the authors is used to compute the hammer performance. This model consists of a set of six differential equations plus a set of twenty non-linear polynomial equations. In addition there are parameter range restrictions given by fabrication and operational standard procedures. In any given application, magnitudes such as power, impact energy, frequency, efficiency and mass flow may be sought for optimality. However these magnitudes must be computed by integration after solving the dynamic model over an entire cycle, thus traditional optimization methods for non-linear equations that are based in gradient information are not suitable. Hence a method that uses secant information is used to approximate the gradient of the space of design variables. Several prototypes using this optimization method have been designed and field tested. The results are in agreement with predicted values.