A maximization algorithm of pseudo-convex quadratic functions
Resumen
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.
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Enkhbat R. and Ibaraki T., On the maximization and minimization of a quasiconvex function. J. Nonlinear Convex Anal., 4, no. 1, 43-76, (2003).
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
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
Best, Michael J. , Quadratic programming with computer programs. Advances in Applied Mathematics. CRC Press, Boca Raton, FL, (2017).
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).
Mangasarian O. L., Pseudo-convex functions. J. Soc. Indust. Appl. Math. Ser. A Control, 3, 281-290, (1965). https://doi.org/10.1137/0303020
Martos B., Quadratic programming with a quasiconvex objective function. Operations Res., 19, 87-97, (1971). https://doi.org/10.1287/opre.19.1.87
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
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
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
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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