Abstract
The most general class of optimization problems is the class of problems where both the objective function and the constraints are nonlinear, as formulated in Eq. (10.1). These problems can be solved by using a variety of methods such as penalty- and barrier-function methods, gradient projection methods, and sequential quadratic-programming (SQP) methods [1]. Among these methods, SQP algorithms have proved highly effective for solving general constrained problems with smooth objective and constraint functions [2]. A more recent development in nonconvex constrained optimization is the extension of the modern interior-point approaches of Chaps. 12–14 to the general class of nonlinear problems.
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References
R. Fletcher, Practical Methods of Optimization, 2nd ed., Wiley, New York, 1987.
P. E. Gill, W. Murray, and M. A. Saunders, “SNOPT: An SQP algorithm for large-scale constrained optimization,” Research Report NA 97-2, Dept. of Mathematics, Univ. of California, San Diego, 1997.
R. B. Wilson, A Simplicial Method for Concave Programming, Ph.D. dissertation, Graduate School of Business Administration, Harvard University, Cambridge, MA., 1963.
P. T. Boggs and J. W. Tolle, “Sequential quadratic programming,” Acta numerica, vol. 4, pp. 1–52, 1995.
G. H. Goluband C. F. Van Loan, Matrix Computation, 2nd ed., Baltimore, The Johns Hopkins University Press, MD, 1989.
S. P. Han, “A globally convergent method for nonlinear programming,” J. Optimization Theory and Applications, vol. 22, pp. 297–309, July 1977.
M. J. D. Powell, “Algorithms for nonlinear constraints that use Lagrangian functions,” Math. Programming, vol. 14, pp. 224–248, 1978.
M. H. Wright, “Direct search methods: Once scorned, now respectable,” in Numerical Analysis 1995, D.F. Griffiths and G. A. Watson eds., pp. 191–208, Addison Wesley Longman, UK.
A. El-Bakry, R. Tapia, T. Tsuchiya, and Y. Zhang, “On the formulation and theory of the Newton interior-point method for nonlinear programming,” J. Optimization Theory and Applications, vol. 89, pp. 507–541, 1996.
A. Forsgren and P. Gill, “Primal-dual interior methods for nonconvex nonlinear programming,” Technical Report NA-96-3, Dept. of Mathematics, Univ. of California, San Diego, 1996.
D. M. Gay, M. L. Overton, and M. H. Wright, “A primal-dual interior method for nonconvex nonlinear programming,” Proc. 1996 Int. Conf. on Nonlinear Programming, Kluwer Academic Publishers, 1998.
R. J. Vanderbei and D. F. Shanno, “An interior-point algorithm for nonconvex nonlinear programming,” Research Report SOR-97-21 (revised), Statistics and Operations Res., Princeton University, June 1998.
D. F. Shanno and R. J. Vanderbei, “Interior-point methods for nonconvex nonlinear programming: Orderings and high-order methods,” Research Report SOR-99-5, Statistics and Operations Res., Princeton University, May 1999.
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(2007). General Nonlinear Optimization Problems. In: Practical Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-71107-2_15
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DOI: https://doi.org/10.1007/978-0-387-71107-2_15
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