Constructing Generalized Mean Functions Using Convex Functions with Regularity Conditions
نویسندگان
چکیده
منابع مشابه
Constructing Generalized Mean Functions Using Convex Functions with Regularity Conditions
The generalized mean function has been widely used in convex analysis and mathematical programming. This paper studies a further generalization of such a function. A necessary and sufficient condition is obtained for the convexity of a generalized function. Additional sufficient conditions that can be easily checked are derived for the purpose of identifying some classes of functions which guar...
متن کاملTo Appear in SIAM Journal of Optimization Constructing Generalized Logarithmic-exponential Functions Using Convex Functions with Regularity Conditions
The logarithmic-exponential (log-exp) function has been widely used in convex analysis and mathematical programming. This paper studies a natural generalization of the log-exp function. Certain necessary and sufficient conditions are obtained for establishing such a generalization. The derived sufficient conditions are explicitly expressed in terms of the first and second derivatives of the fun...
متن کاملGeneralized convex functions and generalized differentials
We study some classes of generalized convex functions, using a generalized di¤erential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdi¤erential or a pseudodi¤erential in the sense of Jeyakumar and Luc. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced...
متن کاملGeneralized convex functions and generalized di¤erentials
We study some classes of generalized convex functions, using a generalized di¤erential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdi¤erential or a pseudodi¤erential in the sense of Jeyakumar and Luc. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced...
متن کاملOn Sequential Optimality Conditions without Constraint Qualifications for Nonlinear Programming with Nonsmooth Convex Objective Functions
Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constrai...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2006
ISSN: 1052-6234,1095-7189
DOI: 10.1137/040603838