Anovelandinteresting approachto infinite andinfinitesimal numberswasrecently proposedin aseriesofpapersandabookbySergeyev.Thisnovelnumeralsystemis basedon the useofanewinfinite unitofmeasure(the numbergrossone, indicated bythe numeral 1 ),thenumberofelementsoftheset,IN, ofnaturalnumbers.Basedontheuseof 1 , De CosmisandDeLeone(2012) havethen proposedanewexactdifferentiablepenaltyfunction for constrainedoptimizationproblems.In this paperthese results arespecializedto theimportant caseofquadraticproblemswithlinear constraints.Moreover,thecrucialrole ofConstraintQualificationconditions(well knowin constraintminimizationliterature) is alsodiscussedwithreferenceto the newproposedpenaltyfunction.
Nonlinear programming and Grossone: Quadratic Programming and the role of Constraint Qualifications
De Leone, R.
2018-01-01
Abstract
Anovelandinteresting approachto infinite andinfinitesimal numberswasrecently proposedin aseriesofpapersandabookbySergeyev.Thisnovelnumeralsystemis basedon the useofanewinfinite unitofmeasure(the numbergrossone, indicated bythe numeral 1 ),thenumberofelementsoftheset,IN, ofnaturalnumbers.Basedontheuseof 1 , De CosmisandDeLeone(2012) havethen proposedanewexactdifferentiablepenaltyfunction for constrainedoptimizationproblems.In this paperthese results arespecializedto theimportant caseofquadraticproblemswithlinear constraints.Moreover,thecrucialrole ofConstraintQualificationconditions(well knowin constraintminimizationliterature) is alsodiscussedwithreferenceto the newproposedpenaltyfunction.| File | Dimensione | Formato | |
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