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Optimality conditions for several type of efficient solutions of set-valued optimization problems

Xuan Duc Ha Truong (txdha***at***math.ac.vn)

Abstract: A simple unified framework is presented for the study of strong efficient solutions, weak efficient solutions, positive proper efficient solutions, Henig global proper efficient solutions, Henig proper efficient solutions, super efficient solutions, Benson proper efficient solutions, Hartley proper efficient solutions, Hurwicz proper efficient solutions and Borwein proper efficient solutions of set-valued optimization problem with/or without constraints. Some versions of the Lagrange claim, the Fermat rule and the Lagrange multiplier rule are formulated in terms of the first- and second- order radial derivatives, the Ioffe approximate coderivative and the Clarke coderivative.

Keywords: Set-valued optimization, efficient solution, proper efficient solution, Lagrange claim, Fermat rule, Lagrange multiplier rule, first- and second- order radial derivatives, Ioffe approximate coderivative, Clarke coderivative.

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: in: P. Pardalos, Th. M. Rassias, A. A. Khan (Eds.), Nonlinear Analysis and Variational Problems, Springer (2010), pp. 305- 324.


Entry Submitted: 01/19/2009
Entry Accepted: 01/19/2009
Entry Last Modified: 08/02/2010

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