Survey of input optimization¹

Characterizing optimality in mathematical programming models

“…(Different initial 0 ° generally result in different optimal inputs 0", even in linear models.) The level of optimization, dealing with such continuous optimization of mathematical models is termed 'input optimization', see [85][86][87][88][89] (abbreviation: IO). In IO the model (P, 0) is considered to be a 'black box', the parameter 0 is the 'input' and the triple {F(0),/~(0),f(0)} is the 'output'.…”

“…In a special case (fixed O), we recover characterizations of optimal solutions for convex models. The results, presented here on optimal inputs, are quite recent (see [73,75,76,88,89]), while those on optimal solutions of convex programs were formulated in the mid-and late seventies and they are a part of the theory formulated by Ben-Israel, Ben-Tal and Zlobec, and their colleagues, see [6,10,80,81] (abbreviated: BBZ). In the presence of extraneous conditions (such as Slater's condition) the BBZ theory recovers the KKT theory of Karush [23,48,55] and Kuhn and Tucker [49] for convex programs.…”

“…Here we follow the approach from [75,76,86,89]. In Section 6 we assume that the model functions are differentiable.…”

Stability of efficiency evaluations in data envelopment analysis

“…Since the objective function is realistic at (0, 0'), and R2(O, 0')=I• L the result is an immediate consequence of Theorem 6.1 from Zlobec (1987) (or the results from the report Semple/Zlobec). 9…”

“…It might be interesting to translate these results into the framework of DEA. Also, note that one may specify 0 = 0' in the model (BL,O,0') and then, starting from some 0 = 0 ~ EI, attempt to calculate an optimal input 0* EI by a numerical method of input optimization (see Zlobec 1987). Such input should identify the most efficient DMU.…”