NONLINEAR PROGRAMMING IN MULTIPLE RESPONSE OPTIMIZATION PROBLEMS.
Themis optimization research program,
TEXAS A AND M UNIV COLLEGE STATION INST OF STATISTICS
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A parametric programming algorithm is developed which will allow one to solve a sequence of closely related convex programming problems sequentially. This algorithm is developed in such a manner as to become an extension to the general convex programming algorithm developed by Hartley and Hocking 1963. In terms of statistical response surface analysis, convex parametric problems arise when it is desirable to simultaneously optimize a number of response surface functions within a given experimental region. In general, this is not possible, however, one may choose to optimize a specified one of these response surface functions subject to the conditions that the others achieve certain desired activity levels. In many situations these activity levels are not clearly defined and a parametric study over several combinations of values of meaningful activity levels is indicated. Extensions of the parametric procedure allows for the solution of non-convex quadratic programming problems with quadratic restrictions in the sense that at least one and usually several local optima are obtained. Combining the parametric study with the ability to handle non-convex functions will allow a thorough analysis of the multiple response problem. Author
- Operations Research