Modelling, Transformations, and Scaling Decisions in Constrained Optimization Problems
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
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This thesis investigates various modelling choices and modelling decisions that can be used by defense analysts when solving nonlinear optimization problems. A discussion is given of separable programming, goal programming, and linear fractional programming models, and a description of the manner by which they can be converted to equivalent linear programs. Transformations of variables recommended in the literature are tested on several well-known test problems using GRG and SUMT nonlinear programming codes. The sensitivity of the GRG code to scaling, rotation of coordinates, and translation of variables is examined. Transformations to obtain separability of variables and experiments using a diagonalization algorithm to transform quadratic expressions into sums of squares are discussed. Barrier and penalty function transformations are also considered.
- Administration and Management
- Operations Research