Abstract
In this review paper, we report recent results in the study of nonlinear unconstrained optimization methods, such as nonlinear penalty function method and nonlinear Lagrangian method. One important feature of this line of research is that unconstrained optimization problems may be nonlinear in the cost function of the original constraint problem. Results such as zero duality gaps, exact penalization, and the existence of nonlinear Lagrange multipliers are reviewed.
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References
Andramonov, M. Yu. (1997), An approach to constructing generalized penalty functions, Research Report 21/97, University of Ballarat.
Burke, J. V. (1991), An exact penalization viewpoint of constrained optimization, SIAM J. Control and Optimization, Vol. 29, pp. 968–998.
Goh, C. J. and Yang, X. Q. (1997), A sufficient and necessary condition for nonconvex constrained optimization, Applied Mathematics Letters, Vol. 10, pp. 9–12.
Goh, C. J. and Yang, X. Q. (1996) A nonlinear Lagrangian theory for nonconvex optimization problems, JOTA (revised).
Rockafellar, R. T. (1993), Lagrange multipliers and optimality, SIAM Review, Vol. 35, pp. 183–238.
Rubinov, A. M. and Glover, B. M. (1997), Duality for increasing positively homogeneous functions and normal sets, RAIRO Operations Research, Vol. 32, pp. 105–123.
Rubinov, A. M. Glover, B. M. and Yang, X.Q. (1997a), Modified Lagrange and penalty functions in continuous optimization, Optimization (to appear).
Rubinov, A. M. Glover, B. M. and Yang, X.Q. (1997b), Decreasing functions with applications to penalization, SIAM Journal on Optimization (to appear).
Rubinov, A. M., Yang, X.Q. and Glover B. M. (1998), Extended Lagrange and penalty functions in optimization, (submitted).
Yang, X.Q. and Li, D. (1999), Successive global optimization method via parametric monotone composition formulation, Journal of Global Optimization, (to appear).
Yevtushenko, Yu. G. and Zhadan, V. G. (1990), Exact auxiliary functions in optimization problems, U.S.S.R Comput. Maths. Math. Phys., Vol. 30, pp. 31–42.
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© 2000 Kluwer Academic Publishers
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Rubinov, A.M., Yang, X.Q., Glover, B.M. (2000). Nonlinear Unconstrained Optimization Methods: A Review. In: Yang, X., Mees, A.I., Fisher, M., Jennings, L. (eds) Progress in Optimization. Applied Optimization, vol 39. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0301-5_4
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DOI: https://doi.org/10.1007/978-1-4613-0301-5_4
Publisher Name: Springer, Boston, MA
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