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Das, Prasanta Kumar The Youngnam Mathematical Society 2017 East Asian mathematical journal Vol.33 No.1
The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.
Prasanta Kumar Das 영남수학회 2017 East Asian mathematical journal Vol.33 No.1
The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized op- timization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, P DA- vector function and P DA-antisymmetric function to show the exis- tence of a new class of function called, (Tη;ξθ)-invex functions. We discuss first and second kind of (Tη;ξθ)-invex functions and establish their exis- tence theorems in ordered topological vector spaces.
ON SUFFICIENT OPTIMALITY THEOREMS FOR NONSMOOTH MULTIOBJECTIVE OPTIMIZATION PROBLEMS
Kim, Moon-Hee,Lee, Gue-Myung Korean Mathematical Society 2001 대한수학회논문집 Vol.16 No.4
We consider a nonsmooth multiobjective opimization problem(PE) involving locally Lipschitz functions and define gen-eralized invexity for locally Lipschitz functions. Using Fritz John type optimality conditions, we establish Fritz John type sufficient optimality theorems for (PE) under generalized invexity.
김성섭(Kim, Seongsup),김태후(Kim, Taehoo),서상택(Seo, Sangtaek) 한국농식품정책학회 2020 농업경영정책연구 Vol.47 No.2
This study sets up a Bonus-Malus System (BMS) in Korean crop insurance to resolve a double loaded penalty in current BMS. The BMS in this study adopts the model suggested by Frangos and Vrontos (2001) with Bayes’ theorem, where initial premium rate is determined by prior distribution but is updated with the loss experience by individual farmers with lapse of time. The concept of fairness suggested by Heras, Vilar and Gil (2002) is adopted to support the BMS developed. For the study, crop insurance data including premium, indemnity and frequency of occurrence provided by NH Property & Casualty Insurance Corporation (the insurer) are used. Among the crops insured only apple and pear are chosen because the two crops have the longest history of crop insurance and ranks the highest insured rate during the program period.