2008
DOI: 10.1016/j.jmaa.2007.04.003
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Continuous minimax optimization using modal intervals

Abstract: Many real life problems can be stated as a continuous minimax optimization problem. Well-known applications to engineering, finance, optics and other fields demonstrate the importance of having reliable methods to tackle continuous minimax problems. In this paper a new approach to the solution of continuous minimax problems over reals is introduced, using tools based on modal intervals. Continuous minimax problems, and global optimization as a particular case, are stated as the computation of semantic extensio… Show more

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Cited by 19 publications
(10 citation statements)
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“…. , X n ) ∈ (TI * (R)) n using the interval extension f * (see Sainz [24,31]) over the α−cuts of the MITFNs X α 1 , . .…”
Section: Interpretability Of the Calculations Definition (Modal Extenmentioning
confidence: 99%
“…. , X n ) ∈ (TI * (R)) n using the interval extension f * (see Sainz [24,31]) over the α−cuts of the MITFNs X α 1 , . .…”
Section: Interpretability Of the Calculations Definition (Modal Extenmentioning
confidence: 99%
“…For this purpose Modal Interval Analysis (MIA) [10] is used. MIA allows proving in computationally efficient way logical formulas by transforming them into an interval inclusion test [11,20]. Table 1 shows a special instance of the QSI algorithm for the given problem.…”
Section: The Qsi Solvermentioning
confidence: 99%
“…This way, it provides tools to verify logical formulas such as the ones in (8) and (9) and, therefore, to tackle problems which can be stated by means of similar logical formulas.…”
Section: F * Algorithmmentioning
confidence: 99%
“…In Section III, the problem of detecting faults is stated as a quantified real constraint satisfaction problem, which can be solved using the modal interval analysis (MIA) [8], [9]. The sliding time windows, which are introduced in the same section, reduce the necessary computational effort and improve the fault-detection results.…”
mentioning
confidence: 99%