Optimization Conditions Of Interval Valued Functions Based On Generalized Derivatives

Calculation error is always a difficult problem in numerical analysis.The accumulation of calculation errors makes the calculation results meaningless.Interval mathematics provides a simple method to keep the calculation results in the required accuracy.Generalized derivative is a generalization of derivative concept under interval valued function,which is of great significance to study the properties of fuzzy systems.This thesis mainly studies the interval valued optimization problem,and finds a set of variables which satisfy the given constraints and makes the objective function the optimal value.First of all,this thesis introduces a derivative,which is more widely used than the generalized Hukuhara derivative.Based on the concept of sub derivative and the convexity of interval valued functions,this thesis further studies the properties of interval valued functions.This thesis further gives the concept of subgradient of multivariate interval valued functions.Combined with the study of convexity of multivariate interval valued functions,a series of Karush-Kuhn-Tucker conditions for interval valued constrained optimization problems under different order relations is studied.Finally,based on the Karush-Kuhn-Tucker condition of interval valued function,this thesis designs a simple algorithm suitable for processing small data.The concept of interval value is introduced into the theory of Support Vector Machine,the concept of interval hyperplane is proposed,the interval separation theorem is obtained,and an interval classification hyperplane is constructed.With the help of the consumption level judgment of 30 sets of data,the effectiveness of this method is illustrated.