Ioffe’s approximate subdifferentials are reviewed and some of his resultsare generalized.An extension of the calculus of the approximate subdifferentials forthe sums to any finite number of functions is provided alon...Ioffe’s approximate subdifferentials are reviewed and some of his resultsare generalized.An extension of the calculus of the approximate subdifferentials forthe sums to any finite number of functions is provided along with a generalizationof the Dubovitzkii-Milyutin theorem.The presentation also indicates some of thelimitations of nonsmooth analysis and optimization.Restriction to the class offunction which is suitable for most of the purposes in nonsmooth optimization issuggested.展开更多
In this paper, we present an existence result for weak efficient solution for the vector optimization problem. The result is stated for invex strongly compactly Lipschitz functions.
This paper refers to Clarke generalized gradient for a smooth composition of max-type functions of the form: f(x) = g(x, maxj∈J1 f1j(x),''', maxj∈Jm fmj(x)), where x ∈Rn, Ji, i = 1,''',m are...This paper refers to Clarke generalized gradient for a smooth composition of max-type functions of the form: f(x) = g(x, maxj∈J1 f1j(x),''', maxj∈Jm fmj(x)), where x ∈Rn, Ji, i = 1,''',m are finite index sets, g and fij,j ∈ Ji, i = 1,... )m, are continuously differentiable on Rm+n and Rn, respectively. In a previous paper) we proposed an algorithm of finding an element of Clarke generalized gradient for f, at a point. In that paper, finding an element of Clarke generalized gradient for f, at a point, is implemented by determining the compatibilities of systems of linear inequalities many times. So its computational amount is very expensive. In this paper) we will modify the algorithm to reduce the times that the compatibilities of systems of linear inequalities have to be determined.展开更多
文摘Ioffe’s approximate subdifferentials are reviewed and some of his resultsare generalized.An extension of the calculus of the approximate subdifferentials forthe sums to any finite number of functions is provided along with a generalizationof the Dubovitzkii-Milyutin theorem.The presentation also indicates some of thelimitations of nonsmooth analysis and optimization.Restriction to the class offunction which is suitable for most of the purposes in nonsmooth optimization issuggested.
基金Ministério de Educacióny Ciencia de Espaa,Grant No.MTM2007-63432
文摘In this paper, we present an existence result for weak efficient solution for the vector optimization problem. The result is stated for invex strongly compactly Lipschitz functions.
基金This project is supported by the Science Function of Liaoning Province.
文摘This paper refers to Clarke generalized gradient for a smooth composition of max-type functions of the form: f(x) = g(x, maxj∈J1 f1j(x),''', maxj∈Jm fmj(x)), where x ∈Rn, Ji, i = 1,''',m are finite index sets, g and fij,j ∈ Ji, i = 1,... )m, are continuously differentiable on Rm+n and Rn, respectively. In a previous paper) we proposed an algorithm of finding an element of Clarke generalized gradient for f, at a point. In that paper, finding an element of Clarke generalized gradient for f, at a point, is implemented by determining the compatibilities of systems of linear inequalities many times. So its computational amount is very expensive. In this paper) we will modify the algorithm to reduce the times that the compatibilities of systems of linear inequalities have to be determined.
