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MultiplierMethod--A General Purpose Algorithm for Nonlinear Programming

Jean-Christophe Culioli
Organization: Centre Automatique et Systemes
Joseph P. Skudlarek
Organization: Cypress Semiconductor Corp
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This is an implementation of the Method of Multipliers (also known as the Augmented Lagrangian Method) due to Hestenes, Powell, Rockafellar and others. It solves nonlinear programming minimization problems with inequality and/or equality constraints. As such, it is a natural generalization of the FindMinimum built-in Mathematica function. See for example D. G. Luenberger, "Linear and Nonlinear Programming" (2nd Ed.), Addison-Wesley, 1984. See also Dimitri P. Bertsekas, "Constrained Optimization and Lagrange Multiplier Methods", Athena Scientific, 1986; and Dimitri P. Bertsekas, "Nonlinear Programming" (2nd Ed.), Athena Scientific, 1999; and Jorge Nocedal and Stephen J. Wright, "Numerical Optimization", Springer-Verlag, 1999.

Updated by Joseph Skudlarek, 15 June 2004.

*Applied Mathematics > Optimization

optimization, objective function, minimize, constraints, equality constraints, linear constraints, nonlinear constraints, equalities, inequalities, augmented Lagrangian, Uzawa algorithm, Primal-Dual method, method of multipliers, multiplier method, quadratic programming, nonlinear optimization, constrained optimization
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MultiplierMethod.m (21.7 KB) - Mathematica package
MultiplierMethod.nb (51.1 KB) - Version 4.2 demo of Multiplier Method [for Mathematica 4.2]
MultiplierMethod.nb (51.7 KB) - Version 5.0 demo of Multiplier Method [for Mathematica 5.0]
MultiplierMethod.nb (51.7 KB) - Version 3.0 demo of Multiplier Method [for Mathematica 3.0]

Files specific to Mathematica 2.2 version:
MultiplierMethod.m (9.2 KB) - Mathematica package
Download (19.2 KB) - Mathematica notebook