In this paper, a pair of second-order mixed symmetric nondifferentiable multiobjective dual programs over arbitrary cones where each of the objective functions contains a pair of support functions is considered. Furth...
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In this paper, by using an augmented Lagrangian approach, we obtain several sufficient conditions for the existence of augmented Lagrange multipliers of a cone constrained optimization problem in Banach spaces, where ...
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In this paper, by using an augmented Lagrangian approach, we obtain several sufficient conditions for the existence of augmented Lagrange multipliers of a cone constrained optimization problem in Banach spaces, where the corresponding augmenting function is assumed to have a valley at zero. Furthermore, we deal with the relationship of saddle points, augmented Lagrange multipliers, and zero duality gap property between the cone constrained optimization problem and its augmented Lagrangian dual problem.
The Markowitz problem consists of finding, in a financial market, a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingal...
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The Markowitz problem consists of finding, in a financial market, a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone constraints: trading strategies must take values in a (possibly random and time-dependent) closed cone. We first prove existence of a solution for convex constraints by showing that the space of constrained terminal gains, which is a space of stochastic integrals, is closed in L-2. Then we use stochastic control methods to describe the local structure of the optimal strategy, as follows. The value process of a naturally associated constrained linear-quadratic optimal control problem is decomposed into a sum with two opportunity processes L-+/- appearing as coefficients. The martingale optimality principle translates into a drift condition for the semimartingale characteristics of L-+/- or equivalently into a coupled system of backward stochastic differential equations for L-+/-. We show how this can be used to both characterize and construct optimal strategies. Our results explain and generalize all the results available in the literature so far. Moreover, we even obtain new sharp results in the unconstrained case.
We introduce a pair of symmetric dual problems for nondifferentiable multiobjective fractional variational problems with cone constraints over arbitrary cones. On the basis of weak efficiency, we obtain symmetric dual...
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Two pairs of non-differentiable multiobjective symmetric dual problems with cone constraints over arbitrary cones, which are Wolfe type and Mond-Weir type, are considered. On the basis of weak efficiency with respect ...
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Two pairs of non-differentiable multiobjective symmetric dual problems with cone constraints over arbitrary cones, which are Wolfe type and Mond-Weir type, are considered. On the basis of weak efficiency with respect to a convex cone, we obtain symmetric duality results for the two pairs of problems under cone-invexity and cone-pseudoinvexity assumptions on the involved functions. Our results extend the results in Khurana [S. Khurana, Symmetric duality in multiobjective programming involving generalized cone-invex functions, European Journal of Operational Research 165 (2005) 592-597] to the non-differentiable multiobjective symmetric dual problem. (C) 2007 Elsevier B.V. All rights reserved.
In the present paper, a pair of Wolfe type nondifferentiable multiobjective second-order symmetric dual programs over arbitrary cones are formulated. Using the concept of weak efficiency with respect to a convex cone,...
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In the present paper, a pair of Wolfe type nondifferentiable multiobjective second-order symmetric dual programs over arbitrary cones are formulated. Using the concept of weak efficiency with respect to a convex cone, weak, strong and converse duality theorems are studied under second-order K-F-convexity assumptions. Self-duality is also discussed. (C) 2010 Elsevier Ltd. All rights reserved.
In this paper, a pair of Mond-Weir type multiobjective higher-order symmetric dual programs over arbitrary cones is formulated and usual duality results are established under higher-order K-preinvexity/K-pseudoinvexit...
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In this paper, a pair of Mond-Weir type multiobjective higher-order symmetric dual programs over arbitrary cones is formulated and usual duality results are established under higher-order K-preinvexity/K-pseudoinvexity assumptions. Symmetric minimax mixed integer primal and dual problems are also discussed. (C) 2010 Elsevier Ltd. All rights reserved.
A pair of multiobjective mixed symmetric dual programs is formulated over arbitrary cones. Weak, strong, converse and self-duality theorems are proved for these programs under K-preinvexity and K-pseudoinvexity assump...
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A pair of multiobjective mixed symmetric dual programs is formulated over arbitrary cones. Weak, strong, converse and self-duality theorems are proved for these programs under K-preinvexity and K-pseudoinvexity assumptions. This mixed symmetric dual formulation unifies the symmetric dual formulations of Suneja et al. (2002) [14] and Khurana (2005) [15]. (C) 2009 Elsevier Ltd. All rights reserved.
A pair of Mond-Weir type multi-objective higher order symmetric dual programs over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under higher order K-F-convexity assumptions...
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A pair of Mond-Weir type multi-objective higher order symmetric dual programs over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under higher order K-F-convexity assumptions. Our results generalize several known results in the literature. (C) 2010 Elsevier Ltd. All rights reserved.
A pair of higher-order Wolfe type and Mond-Weir type multiobjective symmetric dual programs over arbitrary cones is formulated. Weak, strong and converse duality theorems are then established using the notion of highe...
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A pair of higher-order Wolfe type and Mond-Weir type multiobjective symmetric dual programs over arbitrary cones is formulated. Weak, strong and converse duality theorems are then established using the notion of higher-order (F, alpha, rho, d)-convexity/pseudoconvexity assumptions. Special cases are also discussed to show that this paper extends some known results of the literature. (C) 2010 Elsevier Ltd. All rights reserved.
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