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An analysis of some dual problems in multiobjective optimization
- I). Optimization, Volume 53, Number
, 2004
"... In this work we study the duality for a general multiobjective optimization problem. Considering, first, a scalar problem, different duals using the conjugacy approach are presented. Starting from these scalar duals, we introduce six different multiobjective dual problems to the primal one, one depe ..."
Abstract
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Cited by 9 (6 self)
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In this work we study the duality for a general multiobjective optimization problem. Considering, first, a scalar problem, different duals using the conjugacy approach are presented. Starting from these scalar duals, we introduce six different multiobjective dual problems to the primal one, one depending on certain vector parameters. The existence of weak and, under certain conditions, of strong duality between the primal and the dual problems is shown. Afterwards, some inclusion results for the image sets of the multiobjective dual problems (D1), (Dα) and (DF L) are derived. Moreover, we verify that the efficiency sets within the image sets of these problems coincide, but the image sets themselves do not.
Duality for composed convex functions with applications in location theory
- Multi-Criteria- und Fuzzy-Systeme in Theorie und Praxis”, Deutscher Universitäts-Verlag
, 2003
"... location theory ..."
Fenchel-Lagrange versus Geometric Duality in Convex Optimization
"... We present a new duality theory in order to treat convex optimization problems and we prove that the geometric duality used by C.H. Scott and T.R. Jefferson in different papers during the last quarter of century is a special case of it. Moreover, weaker sufficient conditions in order to achieve st ..."
Abstract
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Cited by 5 (4 self)
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We present a new duality theory in order to treat convex optimization problems and we prove that the geometric duality used by C.H. Scott and T.R. Jefferson in different papers during the last quarter of century is a special case of it. Moreover, weaker sufficient conditions in order to achieve strong duality are considered and optimality conditions are derived. Next we apply our approach to some problems considered by Scott and Jefferson, determining their duals. We give weaker sufficient conditions in order to achieve strong duality and the corresponding optimality conditions. Finally, posynomial geometric programming is viewed also as a particular case of the duality approach we present.
Duality for convex partially separable optimization problems
- Mong. Math. J
"... This paper aims to extend duality investigations for the convex partially separable optimization problems. By using the results in [15] we formulate three dual problems for the optimization problem with convex inequality and affine equality constraints, which includes the convex partially separable ..."
Abstract
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Cited by 2 (0 self)
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This paper aims to extend duality investigations for the convex partially separable optimization problems. By using the results in [15] we formulate three dual problems for the optimization problem with convex inequality and affine equality constraints, which includes the convex partially separable one. For these duals we give a constraint qualification which guarantees the existence of strong duality. Optimality conditions for the convex partially separable optimization problem and some particular cases are also obtained.
