[PDF] Top 20 Optimality and Duality for Second-order Multiobjective Variational Problems

... We now prove three results. The first gives Fritz John type necessary conditions for (P) and the remaining two are Kuhn-Tucker type necessary conditions for (P). To establish these necessary conditions, we shall use the ... See full document

... is multiobjective non-linear fractional programming problem involving semilocally convex and related ...of multiobjective fractional programming and corresponding scalar fractional programming ...sufficient ... See full document

... Further, various types of generalizations of convexity theory have played an important role in the evolution of the mathematical programming. During the past decades, the gen- eralizations of convexity were enriched with ... See full document

... sufficient optimality theorem is given by using this characterization and E- convexity ...for multiobjective E-convex ...the multiobjective case are estab- lished under the weakened assumption of the ... See full document

... practical problems encountered in economics, engineering design, and management science, and so forth can be described only by nonsmooth functions, consequently, the theory of nonsmooth optimization using locally ... See full document

... nonsmooth multiobjective programming problems including support functions with inequality and equality ...sufficient optimality conditions are obtained by using higher-order strong convexity for ... See full document

... of multiobjective programming, has grown remarkably in different direc- tional in the setting of optimality conditions and duality theory since ... See full document

... nonsmooth multiobjective programming problems involving locally Lipschitz functions and support ...Karush-Kuhn-Tucker optimality conditions with support functions are ...Sufficient optimality ... See full document

... studied optimality and duality for multiobjective variational ...introduce multiobjective programming in calculus of variation which is a powerful technique for the solutions of various ... See full document

... sufficient optimality conditions for an efficient solution of the nondifferentiable multiobjective fractional programming problem are ...appropriate duality results are proved under higher-order ... See full document

... type optimality conditions for a nondifferentiable multiobjective variational prob- lem are ...type optimality conditions, Mond-weir type second-order nondifferentiable ... See full document

... multitime multiobjective variational problems of minimizing a vector-valued functional of curvilinear integral ...In order to prove the main results in the paper, we introduce the definition of ... See full document

... During the past decades, researchers and practitioners in optimization had a keen interest in approximate solutions of optimization problems. There are several important reasons for considering this kind of ... See full document

... In this paper, we have defined a class of new generalized functions. By using the new functions, we have presented a sufficient optimality condition and Wolfe type duality results for a nondifferentiable ... See full document

... of multiobjective programming, also known as vector programming has grown remarkable in different direction in the setting of optimality condition and duality theory since the ...symmetric ... See full document

... of problems, in pure ...the duality results in the mathematical programming have the ana- logues in calculus of ...constrained variational problem as mathematical programming problem in abstract ... See full document

... the optimality conditions of [1], Tanimoto [2] defined a first-order dual problem of , which gene- ralized the duality theorems for convex minimax pro- gramming problems considered by Weir [3] ... See full document

... The relations (29)-(32) are all deducible from the classical Euler-Lagrange and Clebsch necessary optimality conditions. Particularly, the equations (29)-(32) are the famous Euler-Lagrange differential equation ... See full document

... A multiobjective variational problem involving higher order derivatives is considered and optimality condi- tions for this problem are ...various duality results are validated under ... See full document

... to optimality conditions and duality theorems for the minimax fractional programming ...a duality theorem for convex differen- tiable minimax fractional ...dual problems for minimax fractional ... See full document