THE COMPUTATIONAL ASPECTS OF POSTOPTIMAL ANALYSIS OF GEOMETRIC PROGRAMS
AuthorStiglich, George Randall
Differential equations -- Numerical solutions -- Computer programs.
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PublisherThe University of Arizona.
RightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
AbstractOptimal engineering design specifications are usually derived from an iterative design process. Here, different mathematical programs, each representing a particular problem assumption, are solved in order to gain insight into how and why an ideal design changes as model parameters vary. The mathematical technique used in this process is termed sensitivity analysis. The focus of this study is on techniques for performing such analysis on optimization problems which can be modeled as geometric programs. A dual based computationally attractive numerical procedure was developed to generate the locus of optimal solutions to prototype geometric programs corresponding to a large set of program parameter trajectories. Coefficient variation can include individual or simultaneous changes in any or all cost and exponent values. Sensitivity analysis is accomplished by numerically solving a specially constructed nonlinear initial value differential equation problem. Computational procedures were developed for computing an intitial value point, differential equation construction and solution, primal/dual conversion and problem reconstruction in the event of a primal constraint status change. A computer program written to carry out this scheme was described and used in the design of a batch process chemical plant. Preliminary results show the sensitivity analysis procedure developed in this study is attractive in terms of required computation time and perturbation flexibility of model coefficients.
Degree ProgramGraduate College
Systems and Industrial Engineering