Quadratic programming on the positive orthant with a quasiconvex objective function
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2019-07-31
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Universidade Federal de Goiás
Resumo
In this work, we will study a class of real symmetric matrices that we will call subdefinite, these matrices include the positive semidefinites. For our purpose we will focus on the merely positive subdefinite matrices, that is, those matrices that are positive subdefinite but are not positive semidefinite. We will discuss the quadratic functions on Rn + and show that these functions are quasiconvex not convex, when their matrix representation is given by a merely positive subdefinite matrix. In addition, we will present a result of great importance in quadratic programming given that it allows to reduce the quasiconvexity of these nonconvex quadratic functions to the pseudoconvexity in the semipositive orthant. Finally, we will study the conditional gradient method to solve the quadratic programming problem, where the objective function is of this type.
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ZUÑIGA, R. Y. C. Quadratic programming on the positive orthant with a quasiconvex objective function. 2019. 82 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2019.