Abstract
THE PRIMARY INTENT OF this chapter is to introduce the reader to the theoretical foundations of nonlinear programming. Particularly important are the notions of local and global optimality in mathematical programming, the Kuhn-Tucker necessary conditions for optimality in nonlinear programming, and the role played by convexity in making necessary conditions sufficient. The following is an outline of the principal topics covered in this chapter:
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2.12 References and Additional Reading
Armacost, R., & Fiacco, A. V. (1974). Computational experience in sensitivity analysis for nonlinear programming. Mathematical Programming, 6, 301–326.
Armacost, R., & Fiacco, A. V. (1978). Sensitivity analysis for parametric nonlinear programming using penalty methods. Computational and Mathematical Programming, 502, 261–269.
Avriel, M. (1976). Nonlinear programming: Analysis and applications. Englewood Cliffs, NJ: PrenticeHall.
Bazarra, M. S., Sherali, H. D., & Shetty, C. M. (2006). Nonlinear programming: Theory and algorithms. Hoboken, NJ: John Wiley
Fiacco, A. V. (1983) Introduction to sensitivity and stability analysis in nonlinear programming, (367 pp.) New York: Academic.
Fiacco, A. V. (1973). Sensitivity analysis for nonlinear programming using penalty methods. Technical Report, Serial no. T-275, Institution for Management Science and Engineering, The George Washington University.
Fiacco, A. V., & McCormick G. P. (1968). Nonlinear programming: Sequential unconstrained minimization techniques. New York: John Wiley.
Hestenes, M. R. (1975). Optimization theory: the finite dimensional case. (464Â pp.) New York: Wiley.
Mangasarian, O. (1969). Nonlinear programming. New York: McGraw-Hill.
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Friesz, T.L., Bernstein, D. (2016). Elements of Nonlinear Programming. In: Foundations of Network Optimization and Games. Complex Networks and Dynamic Systems, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7594-2_2
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