Abstract
We consider the approximation of the objective function by a linear functional in a partially defined optimization problem, when the objective function is partially defined by comparison of its values on some set of vectors from the feasible region. A necessary and sufficient condition is given for the existence of an approximating linear functional and a method of estimating its coefficients by a linear correction procedure is proposed.
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References
V. I. Donskoi, "Partially defined optimization problems: an approach to solution based on pattern recognition theory," Dinamicheskie Sistemy, No. 8, pp. 71–77 (1989).
V. D. Mazurov, "Optimization problem with a poorly formalized objective," in: Parametric Optimization and Approximation Methods of Improper Mathematical Programming Problems [in Russian], Sverdlovsk (1985), pp. 51–53.
Additional information
Simferopol' University. Translated from Dinamicheskie Sistemy, No. 10, pp. 117–123, 1992.
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Rudenko, L.I. Objective functional approximation in a partially defined optimization problem. J Math Sci 72, 3359–3363 (1994). https://doi.org/10.1007/BF01261697
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DOI: https://doi.org/10.1007/BF01261697