ALGORITHMIC PROBLEMS IN FACTORABLE PROGRAMMING WITH APPLICATION TO SOLUTION OF A NONLINEAR PROGRAMMING PROBLEM IN SYSTEMS DYNAMICS

This work is concerned with algorithmic and computational problems that arise when a computer code based on the Sequential Unconstrained Minimization Technique and factorable functions is used to solve a nonlinear programming problem in systems dynamics.; The usual representation of the dynamic optimization problem in factorable form requires a large number of repetitive blocks of input files. An indexing capability, paralleling that used by the FORTRAN compiler, is developed to reduce the size of the input and facilitate the user representation of the dynamic model.; The dynamic structure of the model gives rise to an inordinate number of dyads to represent the Hessian matrices. A procedure to reduce the number of outer product forms that requires little computational effort is developed. This allows the efficient solution of the model using Newton's method.; An indirect method is devised to allow sensitivity and elasticity analysis in situations in which the parameters of the problem are dependent on an underlying set of parameters.; An algorithm based on cubic and quartic approximations to the step-size problem is developed. This speeds convergence and also allows for satisfactory resolution of the difficulties associated with using directions of nonpositive curvature of the step-size function in a modified Newton method. The radius and rate of convergence of this algorithm are analyzed in detail.