A construction method in parametric programming

We consider a linear programming problem, with two parameters in the objective function, and present an algorithm for finding the decomposition of the parameter space into maximal polyhedral areas in which particular basic solutions are optimal. Special attention is paid to fill up areas of degenerate solutions.     

Parametric optimal design

Two algorithms for the solution of a parametric optimal design problem are developed and applied to example problems from diverse fields, such as finite allocation problems, optimal design of dynamical systems, and Chebyshev approximation. Sensitivity analysis gives rise to a first-order feedback law, which contains a compensating term for any error in the nominal solution, as well as sensitivity of the solution with respect to design parameters. The compensating term, when used alone, leads to a new second-order method of maximization for a linearly-constrained nonlinear programming problem.This paper is based on the PhD Thesis of the first author.     

Parametric excitation of hybrid mode in magnetised piezoelectric semiconductors

Using the hydrodynamic model of homogeneous plasma, the parametric decay of a laser beam into an acoustic wave and another electromagnetic wave has been studied in heavily dopedn-type piezoelectric semiconductors in the presence of a transverse magnetostatic field. This decay process results in the parametric excitation of the hybrid mode. The threshold electric field necessary for the onset of instability equals to zero. The magnetostatic field couples the acoustic and the electromagnetic waves and in its absence the instability disappears. The growth rate increases with the square of the magnetic field.     

Parametric instability of a rotating truncated conical shell subjected to periodic axial loads

Parametric instability of a rotating truncated conical shell subjected to periodic axial loads is studied in the paper. Through deriving accurate expressions of inertial force and initial hoop tension, a rotating conical shell model is presented based upon the Love's thin shell theory. Considering the periodic axial loads, equations of motion of the system with periodic stiffness coefficients are obtained utilizing the generalized differential quadrature (GDQ) method. Hill's method is introduced for parametric instability analysis. Primary instability regions for various natural modes are computed. Effects of rotational speed, constant axial load, cone angle and other geometrical parameters on the location and width of various instability regions are examined.     

Complexity of some parametric integer and network programming problems

Two examples of parametric cost programming problems—one in network programming and one in NP-hard 0-1 programming—are given; in each case, the number of breakpoints in the optimal cost curve is exponential in the square root of the number of variables in the problem. This research is partially supported by the Air Force Office of Scientic Research. Air Force Number AFOSR-78-3646     

One-parameter families of optimization problems: Equality constraints

In this paper, we introduce generalized critical points and discuss their relationship with other concepts of critical points [resp., stationary points]. Generalized critical points play an important role in parametric optimization. Under generic regularity conditions, we study the set of generalized critical points, in particular, the change of the Morse index. We focus our attention on problems with equality constraints only and provide an indication of how the present theory can be extended to problems with inequality constraints as well.     

Second order sensitivity analysis and asymptotic theory of parametrized nonlinear programs

In this paper we study second-order differential properties of an optimal-value function(x). It is shown that under certain conditions(x) possesses second-order directional derivatives, which can be calculated by solving corresponding quadratic programs. Also upper and lower bounds on these derivatives are introduced under weaker assumptions. In particular we show that the second-order directional derivative is infinite if the corresponding quadratic program is unbounded. Finally sensitivity results are applied to investigate asymptotics of estimators in parametrized nonlinear programs.     

Parametric or non-parametric statistical tools applied to marine aerosol sampling

Atmospheric aerosol sampling has been performed in parallel with both high and low air flows. A comparison of the results requires proper statistical design and analysis. The presence of several outliers and the increase of residuals with increasing concentration have led to the recommendation of handling the data with non-parametric methods rather than parametric statistical analysis.Conversion equations were obtained for each of the ionic species examined for prediction of low air flow sampling from long-term observations with high air flow sampling.     

On the parametric linear complementarity problem: A generalized solution procedure

This paper presents a solution procedure for the parametric linear complementarity problemIw–Mz=q+sp,w ^T z=0,w0, andz0, whereM is a positive semidefinite matrix or aP-matrix. This procedure is different from existing ones in the way it handles initialization. By exploiting special relationships between the vectorsq andp, it can reduce computational effort. Sinceq is an arbitrary vector, the procedure can be used for the ordinary linear complementarity problem. In that case, it produces pivots exactly analogous to those of Lemke's algorithm.This paper is based on the author's doctoral dissertation at Johns Hopkins University, 1977. The author wishes to thank her advisors, Professors C. S. ReVelle and D. J. Elzinga. During the last year of her graduate studies, the author held an AAUW-IBM dissertation fellowship.