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Survey of input optimization. (English) Zbl 0633.90077
Input optimization is a conceptually new level of optimization, at which the mathematical programming model, rather than a usual program, is optimized. This is achieved by optimizing the optimal value function by stable perturbations of the parameters (input).
This paper is a survey of the basic ideas in finite-dimensional input optimization for both single- and multi-objective linear and convex models. The theory is general enough not to require extraneous assumptions, such as linear independence of the gradients or Slater’s condition. On the other hand, it is of a constructive nature that makes it possible to formulate numerical methods for computing an “optimal input” and the corresponding “optimal realization” of the mathematical model. Many results from the “usual” mathematical programming and sensitivity analysis follow as special cases.
The paper contains many illustrative examples and lists a wide range of (potential) applications of input optimization, from long-range planning for an economic system and selection of the most “suitable” mathematical programming model, to optimization of engineering designs and new numerical methods for solving nonlinear programs. Economic interpretations of selected theoretical results reaffirm that stable systems necessarily move towards less restricted states and that the underlying continuous behavioural structure of economic and management phenomena is in fact oscillatory.

MSC:
90C31 Sensitivity, stability, parametric optimization
65K05 Numerical mathematical programming methods
91B62 Economic growth models
90C30 Nonlinear programming
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