Primal or dual strong-duality in nonconvex optimization and a class of quasiconvex problems having zero duality gap
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Primal or dual strong-duality (or min-sup, inf-max duality) in nonconvex optimization is revisited in view of recent literature on the subject, establishing, in particular, new characterizations for the second case. This gives rise to a new class of quasiconvex problems having zero duality gap or closedness of images of vector mappings associated to those problems. Such conditions are described for the classes of linear fractional functions and that of quadratic ones. In addition, some applications to nonconvex quadratic optimization problems under a single inequality or equality constraint, are presented, providing new results for the fulfillment of zero duality gap or dual strong-duality.
KeywordsZero duality gap Strong duality Linear fractional programming Quasiconvex programming Quadratic programming
Mathematics Subject Classification90C20 90C46 49N10 49N15 52A10
The research for the first author was supported by the Programa Nacional de Innovación para la Competitividad y Productividad (Innóvate Perú), under contract 013-INNOVATEPERU-ECIP-2016, and was carried out partially while he was visiting IMCA-UNI during 2016. He is grateful for the hospitality of its members. The research material of this work was also supported in part by FONDECYT 115-0973 (Chile) and Basal project, CMM, Universidad de Chile, for the first author; whereas the fourth author was supported by FONDECYT 182-2015 (Perú), and part of his research was carried out while visited University of Concepcion. The authors want to express their gratitude to the referee for his/her careful reading of the manuscript and criticism, which were taken into account in the present version.
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