Convergence of a continuous approach for zero-one programming problems |
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Authors: | Yanyan Li Tao TanXingsi Li |
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Institution: | a College of Science, Shandong University of Science and Technology, Shandong 266510, China b State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China |
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Abstract: | In this paper a new continuous formulation for the zero-one programming problem is presented, followed by an investigation of the algorithm for it. This paper first reformulates the zero-one programming problem as an equivalent mathematical programs with complementarity constraints, then as a smooth ordinary nonlinear programming problem with the help of the Fischer-Burmeister function. After that the augmented Lagrangian method is introduced to solve the resulting continuous problem, with optimality conditions for the non-smooth augmented Lagrangian problem derived on the basis of approximate smooth variational principle, and with convergence properties established. To our benefit, the sequence of solutions generated converges to feasible solutions of the original problem, which provides a necessary basis for the convergence results. |
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Keywords: | Zero-one programming problems Boolean variables Fischer-Burmeister function Optimality condition |
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