Abstract
In this work, we propose a global optimization approach for mixed-integer programming problems. To this aim, we preliminarily define an exact penalty algorithm model for globally solving general problems and we show its convergence properties. Then, we describe a particular version of the algorithm that solves mixed-integer problems and we report computational results on some MINLP problems.
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Abello J., Butenko S., Pardalos P.M., Resende M.: Finding independent sets in a graph using continuous multivariable polynomial formulations. J. Glob. Optim. 21, 111–137 (2001)
Adjiman C.S., Dallwig S., Floudas C.A., Neumaier A.: A global optimization method, α-BB, for general twice-differentiable constrained NLPs I. Theoretical Advances. Comput. Chem. Eng. 22, 1137–1158 (1998)
Adjiman C.S., Androulakis I.P., Floudas C.A.: A global optimization method, α-BB, for general twice-differentiable constrained NLPs II. Implementation and computational results. Comput. Chem. Eng. 22, 1159–1179 (1998)
Balasundaram B., Butenko S.: Constructing test functions for global optimization using continuous formulations of graph problems. Optim. Methods Softw. 20, 439–452 (2005)
Borchardt M.: An exact penalty approach for solving a class of minimization problems with Boolean variables. Optimization 19(6), 829–838 (1988)
Floudas, C.A., Pardalos, P.M., Adjiman, C., Esposito, W.R., Gms, Z.H., Harding, S.T., Klepeis, J.L., Meyer, C.A., Schweiger, C.A.: Handbook of test problems in local and global optimization handbook of test problems in local and global optimization. Nonconvex Optimization and its Applications (closed), vol. 33 (1999)
Giannessi F., Niccolucci F.: Connections between nonlinear and integer programming problems. Symposia Mathematica, vol. 19., pp. 161–176. Academic Press, New York (1976)
Horst R., Pardalos P.M., Thoai N.V.: Introduction to Global Optimization, 2nd edn. Kluwer, Dordrecht (2000)
Kalantari B., Rosen J.B.: Penalty formulation for zero-one integer equivalent problem. Math. Progr. 24, 229–232 (1982)
Kalantari B., Rosen J.B.: Penalty formulation for zero-one nonlinear programming. Discret. Appl. Math. 16(2), 179–182 (1987)
Jones D.R., Perttunen C.D., Stuckman B.E.: Lipschitzian optimization without the lipschitz constant. J. Optim. Theory Appl. 79(1), 157–181 (1993)
Jones D.R.: The DIRECT global optimization algorithm. In: Floudas, C., Pardalos, P. (eds.) Encyclopedia of Optimization, pp. 431–440. Kluwer Academic Publishers, Dordrecht (2001)
Liuzzi, G., Lucidi, S., Piccialli, V.: A partition-based global optimization algorithm. J. Glob. Optim (2009). doi:10.1007/s10898-009-9515-y
Lucidi S., Rinaldi F.: Exact penalty functions for nonlinear integer programming problems. J. Optim. Theory Appl. 145(3), 479–488 (2010)
Mangasarian O.L.: Knapsack feasibility as an absolute value equation solvable by successive linear programming. Optim. Lett. 3(2), 161–170 (2009)
Murray W., Ng K.M.: An algorithm for nonlinear optimization problems with binary variables. Comput. Optim. Appl. 47(2), 257–288 (2010)
Pardalos, P.M., Prokopyev, O.A., Busygin, S.: Continuous approaches for solving discrete optimization problems. In: Handbook on Modelling for Discrete Optimization, vol. 88. Springer, US (2006)
Raghavachari M.: On connections between zero-one integer programming and concave programming under linear constraints. Oper. Res. 17(4), 680–684 (1969)
Rinaldi F.: New results on the equivalence between zero-one programming and continuous concave programming. Optim. Lett. 3(3), 377–386 (2009)
Tawarmalani M., Sahinidis N.V.: Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming. Theory, Algorithm, Software and Applications. Kluwer Academic Publishers, Dordrecht (2002)
Tawarmalani M., Sahinidis N.V.: A polyhedral branch-and-cut approach to global optimization. Math. Progr. 103(2), 225–249 (2005)
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Lucidi, S., Rinaldi, F. An exact penalty global optimization approach for mixed-integer programming problems. Optim Lett 7, 297–307 (2013). https://doi.org/10.1007/s11590-011-0417-9
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DOI: https://doi.org/10.1007/s11590-011-0417-9