A maximization algorithm of pseudo-convex quadratic functions
DOI:
https://doi.org/10.5269/bspm.48303Abstract
We give an algorithm to find maxima of pseudo-convex quadratic functions on closed convex sets and show its convergence. Some computational results are given at the end.
References
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2. Ferland J. A., Maximal domains of quasi-convexity and pseudo-convexity for quadratic functions. Math. Programming, 3, 178-192, (1972). https://doi.org/10.1007/BF01584988
3. Greub W. H., Linear Algebra. Fourth edition. Graduate Texts in Mathematics, No. 23., Springer-Verlag, New YorkBerlin, (1975). https://doi.org/10.1007/978-1-4684-9446-4
4. Best, Michael J. , Quadratic programming with computer programs. Advances in Applied Mathematics. CRC Press, Boca Raton, FL, (2017).
5. Hassouni A. and Jaddar A., On generalized monotone multifunctions with applications to optimality conditions in generalized convex programming. J. Inequal. Pure Appl. Math., 4, no. 4, Article 67, 11 pp., (2003).
6. Mangasarian O. L., Pseudo-convex functions. J. Soc. Indust. Appl. Math. Ser. A Control, 3, 281-290, (1965). https://doi.org/10.1137/0303020
7. Martos B., Quadratic programming with a quasiconvex objective function. Operations Res., 19, 87-97, (1971). https://doi.org/10.1287/opre.19.1.87
8. Rentsen E., An algorithm for maximizing a convex function over a simple set. J. Global Optim., 8, no. 4, 379-391, (1996). https://doi.org/10.1007/BF02403999
9. Schaible S., Second-order characterizations of pseudoconvex quadratic functions. J. Optim. Theory Appl., 21, no. 1, 15-26, (1977). https://doi.org/10.1007/BF00932540
10. Schaible S., Quasiconvex, pseudoconvex, and strictly pseudoconvex quadratic functions. J. Optim. Theory Appl., 35, no. 3, 303-338, (1981). https://doi.org/10.1007/BF00934906
11. Press W. H.; Teukolsky S. A.; Vetterling W. T. and Flannery B. P., Numerical recipes in Fortran 77. The art of scientific computing, second edition. Cambridge University Press, Cambridge, (1996).
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2022-02-02
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