In this study, we convert a bilevelquadraticprogramming problem (BQPP) into single-level mathematical programming with complementary constraints (MPCC), utilizing the Karush-Kuhn-Tucker (KKT) theorem. We address the...
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ISBN:
(纸本)9789819743988;9789819743995
In this study, we convert a bilevelquadraticprogramming problem (BQPP) into single-level mathematical programming with complementary constraints (MPCC), utilizing the Karush-Kuhn-Tucker (KKT) theorem. We address the inherent nonconvexity of MPCC by applying the linear transformation, which effectively relaxes the complementary slackness conditions to semi-positive definite quadratic constraints, thereby facilitating the transformation of the problem into convexprogramming. Furthermore, we introduce a projection neural network designed for resolving the MPCC efficiently. This neural network is structured to guarantee convergence from any initial point to the optimal solution of the original problem. The efficacy of our methodology is validated through a numerical simulation.
This paper presents a neurodynamic optimization approach to bilevelquadraticprogramming (BQP). Based on the Karush-Kuhn-Tucker (KKT) theorem, the BQP problem is reduced to a one-level mathematical program subject to...
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This paper presents a neurodynamic optimization approach to bilevelquadraticprogramming (BQP). Based on the Karush-Kuhn-Tucker (KKT) theorem, the BQP problem is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). It is proved that the global solution of the MPCC is the minimal one of the optimal solutions to multiple convex optimization subproblems. A recurrent neural network is developed for solving these convex optimization subproblems. From any initial state, the state of the proposed neural network is convergent to an equilibrium point of the neural network, which is just the optimal solution of the convex optimization subproblem. Compared with existing recurrent neural networks for BQP, the proposed neural network is guaranteed for delivering the exact optimal solutions to any convex BQP problems. Moreover, it is proved that the proposed neural network for bilevel linear programming is convergent to an equilibrium point in finite time. Finally, three numerical examples are elaborated to substantiate the efficacy of the proposed approach.
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