Abstract
We introduce a discrete penalty called Boolean Penalty to 0–1 constrained nonlinear programming (PNLC-01). The main importance of this Penalty function are its properties which allow us to develop algorithms for the PNLC-01 problem. Optimality conditions, and numerical results are presented.
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References
Balas, E. and Mazzola, J. (1984), Nonlinear 0–1 programming: I. Linearization Techniques, Mathematical Programming 30: 1-21.
Cha, J., Mixed Discrete Constrained Nonlinear Programming, Ph.D. Thesis, University of New York at Buffalo, 1987.
Cha, J.Z. and Mayne, R.W. (1987), Mixed Discrete Constrained Nonlinear Programming via Recursive Quadratic Formula with Rank-One Update Formula.Post-Doctoral Fellow, National Center Earthquake Engineering Research, Buffalo, New York.
Fletcher, R. and Leyffer, S. (1994), Solving mixed integer nonlinear programs by outer approximation, Mathematical Programming 66: 327–349.
Garfinkel, R.S. and Nemhauser, G.L. (1972), Integer Programming, John Wiley & Sons, New York, NY.
Glover, F. and Woosley, E. (1974), Converting the 0–1 polynomial programming problems to a 0-1 linear program, Operation Research 22, 180-182.
Gupta, O. (1980), Branch and Bound Experiment in Nonlinear Integer Programming, Ph.D. Thesis, School of Industrial Engineering, Purdue University, West Lafayette, IN.
Gupta, O. and Ravindran, A., Nonlinear integer programming algorithms: a survey,Working Paper No. 8005, College of Business and Economics,Washington State University, Pullman, Washington 99164.
Hammer, P.L. and Rudeanu, S. (1968), Boolean Method in Operation Research and Related Area. Springer Verlag, New York, NY.
Hansen, P. (1979), Methods of nonlinear 0–1 programming, Discrete Applied Mathematics 5, 53-70.
Hansen, P., Jaumard, B. and Mathon, V. (1993), Constrained nonlinear 0–1 programming, ORSA Journal on Computing 5: 97-119.
Kiwiel, K. (1995), Proximal level bundle methods for convex nondifferentiable optimization, saddle-point problems and variational inequalities, Mathematical Programming 69: 89–104.
Lemarechal, C., Nemyrovskii, A. and Nesterov, Y. (1995), New variant of bundle methods, Mathematical Programming 69: 111–147.
Loh, H. and Papalambros, P. (1989), A sequential linearization approach for solving mixed-discrete nonlinear design optimization problems, Technical Report, UM-MEAM–89-08, Design Laboratory, University of Michigan.
Mauricio, D., Métodos de Resolução de Problemas da Programação Não Linear Inteira, Ph.D. Thesis, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, 1994.
Mauricio, D., Maculan, N. and Scheimberg, S. (1994), An efficient cutting plane for 0–1 nonlinear programming, Publicação Técnica Interna LCENG/Universidade Estadual do Norte Fluminese, Rio de Janeiro.
Wu, Z. (1991), A Subgradient Algorithm for Nonlinear Integer Programming and Its Parallel Implementation. Ph.D. Thesis, Dept. of Math. Sci., Rice University, Houston.
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Mauricio, D., Maculan, N. A Boolean Penalty Method for Zero-One Nonlinear Programming. Journal of Global Optimization 16, 343–354 (2000). https://doi.org/10.1023/A:1008329405026
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DOI: https://doi.org/10.1023/A:1008329405026