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A logarithmic descent direction algorithm for the quadratic knapsack problem. (English) Zbl 1433.90105
Summary: The quadratic knapsack problem is an NP-hard optimization problem with many diverse applications in industrial and management engineering. However, computational complexities still remain in the quadratic knapsack problem. In this study, a logarithmic descent direction algorithm is proposed to approximate a solution to the quadratic knapsack problem. The proposed algorithm is based on the Karush-Kuhn-Tucker necessary optimality condition and the damped Newton method. The convergence of the algorithm is proven, and the numerical results indicate its effectiveness.
MSC:
90C20 Quadratic programming
65K10 Numerical optimization and variational techniques
90C51 Interior-point methods
90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
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