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Abstract
In this short paper, we recall the use of squared slacks used to transform inequality constraints into equalities and several reasons why their introduction may be harmful in many algorithmic frameworks routinely used in nonlinear programming. Numerical examples performed with the sequential quadratic programming method illustrate those reasons. Our results are reproducible with state-of-the-art implementations of the methods concerned and mostly serve a pedagogical purpose, which we believe will be useful not only to practitioners and students, but also to researchers.
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References
- BERTSEKAS, D. 1996. Constrained Optimization and Lagrange Multiplier Methods. Athena Scientific, Belmont MA, USA.
- BERTSEKAS, D. 1999. Nonlinear Programming (2nd edition). Athena Scientific, Belmont MA, USA.
- BOGGS, P.T. and TOLLE, J.W. 1995. Sequential quadratic programming. Acta Numerica, 4: 1–51.
- GILL, P.E., MURRAY, W. and WRIGHT, M. 1981. Practical Optimization. Academic Press, London.
- GOLUB, G.H. and VAN LOAN, C.F. 1996. Matrix Computations (3rd edition). Johns Hopkins University Press, Baltimore, MD, USA.
- NASH, S.G. 1998. SUMT (Revisited). Operations Research, 46: 763–775.
- NOCEDAL, J. and WRIGHT, S.J. 1999. Numerical Optimization. Springer series in Operations Research. Springer-Verlag, New York, USA.
- TAPIA, R.A. 1980. On the role of slack variables in quasi-Newton methods for constrained optimization. In L.C.W. DIXON and G.P. SZEGÖ (eds.) Numerical Optimization of Dynamic Systems, pp. 235–246. North Holland Publishing Company.
References
BERTSEKAS, D. 1996. Constrained Optimization and Lagrange Multiplier Methods. Athena Scientific, Belmont MA, USA.
BERTSEKAS, D. 1999. Nonlinear Programming (2nd edition). Athena Scientific, Belmont MA, USA.
BOGGS, P.T. and TOLLE, J.W. 1995. Sequential quadratic programming. Acta Numerica, 4: 1–51.
GILL, P.E., MURRAY, W. and WRIGHT, M. 1981. Practical Optimization. Academic Press, London.
GOLUB, G.H. and VAN LOAN, C.F. 1996. Matrix Computations (3rd edition). Johns Hopkins University Press, Baltimore, MD, USA.
NASH, S.G. 1998. SUMT (Revisited). Operations Research, 46: 763–775.
NOCEDAL, J. and WRIGHT, S.J. 1999. Numerical Optimization. Springer series in Operations Research. Springer-Verlag, New York, USA.
TAPIA, R.A. 1980. On the role of slack variables in quasi-Newton methods for constrained optimization. In L.C.W. DIXON and G.P. SZEGÖ (eds.) Numerical Optimization of Dynamic Systems, pp. 235–246. North Holland Publishing Company.