Article Outline
Introduction
Definitions
Formulations
Representing the Discrete Decisions by Approximate Continuous Variables
Representing the Discrete Decisions by Exact Continuous Variables
Modeling Propositional Logic Constraints with Exact Continuous Variables
The Case of Inconsistent Equalities
Conclusions
See also
References
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bazaraa M, Sherali H, Shetty C (1993) Nonlinear Programming. Wiley, Hoboken, New Jersey
Chen B, Chen X, Kanzow C (2000) A penalized Fischer–Burmeister NCP-function. Math Program 88:211–216
Floudas CA (1995) Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications. Oxford University Press, New York
Giannesi F, Niccolucci F (1976) Connections between nonlinear and integer programming problems. In: Institut Nazionale di Alta Mathematica (ed) Symposia Mathematica, vol XIX. Acad. Press, New York, pp 161–176
Grossmann IE, Hooker J (2000) Logic based approaches for mixed integer programming models and their application in process synthesis. In: Malone M, Trainham J, Carnahan B (eds) Foundations of Computer-Aided Process Design 323. AIChE Symp. Series. CACHE Publications, Austin, Texas, pp 70–83
Jongen HT, Weber G-W (1991) Nonlinear optimization: characterization of structural stability. J Glob Optim 1:47–64
Leyffer S (2006) Complementarity constraints as nonlinear equations: theory and numerical experiences. In: Dempe S, Kalashnikov V (eds) Optimization and Multivalued Mappings. Springer, Dordrecht, pp 169–208
Luo Z, Pang J, Ralph D (1996) Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge
Pardalos PM (1994) The linear complementarity problem. In: Gomez S, Hennart JP (eds) Advances in Optimization and Numerical Analysis. Springer, New York, pp 39–49
Pardalos PM, Prokopyev OA, Busygin S (2006) Continuous approaches for solving discrete optimization problems. In: Appa G, Pitsoulis L, Williams HP (eds) Handbook on Modelling for Discrete Optimization. Springer, New York, pp 39–60
Raghunathan A, Biegler L (2003) Mathematical programs with equilibrium constraints (MPEC) in process engineering. Comp Chem Eng 27(10):1381–1392
Raman R, Grossmann IE (1994) Modelling and computational techniques for logic based integer programming. Comput Chem Eng 18(7):563–578
Robinson S (1976) Stability theory for systems of inequalities, part II: differentiable nonlinear systems. SIAM J Numer Anal 13:497–513
Scheel H, Scholtes S (2000) Mathematical programs with complementarity constraints: stationarity, optimality, and sensitivity. Math Oper Res 25:1–22
Stein O, Oldenburg J, Marquardt W (2004) Continuous reformulations of discrete-continuous optimization problems. Comput Chem Eng 28:1951–1966
Stubbs R, Mehrotra S (1999) A branch-and-cut method for 0-1 mixed convex programming. Math Program 86:515–532
Vecchietti A, Lee S, Grossmann IE (2003) Modeling of discrete/continuous optimization problems: characterization and formulation of disjunctions and their relaxations. Comput Chem Eng 27(3):433–448
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag
About this entry
Cite this entry
Stein, O. (2008). Continuous Reformulations of Discrete-Continuous Optimization Problems . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_90
Download citation
DOI: https://doi.org/10.1007/978-0-387-74759-0_90
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-74758-3
Online ISBN: 978-0-387-74759-0
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering