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New results in optimization with functional constraints
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New results in optimization with functional constraints
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ETD_1769
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051899
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eng
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theses
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Operations Research
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Topic
Mathematical optimization
Abstract
We consider optimization problems featuring nonnegativity constraints on functions associated with the decision variables. The first part of the thesis is devoted to the topic of optimization over the cone of positive polynomials. We present a method for constructing non-negative spline approximations to the arrival rate of a non-homogenous Poisson process based on observed arrival data, along with numerical results and a comparison to previous approaches. Our results are obtained by formulating the problem as a
semidefinite program; we explore the theoretical obstacles to a more direct method by proving that only a constant number of linearly independent bilinear optimality conditions exist for cones of positive polynomials, regardless of dimension.
In the second part we look at optimization with second order stochastic dominance constraints. Here the functional inequalities appear naturally, featuring the integral of the distribution function of a random variable defined by the decision variables. We develop new duality results as well as cutting plane methods that
are shown to perform well on a class of portfolio optimization problems. Finally we point out an interesting connection, arising as part of our duality considerations, between the theory of measures with given marginals and network feasibility. This results in a new proof of Strassen's Theorem from its trivial discrete case.
semidefinite program; we explore the theoretical obstacles to a more direct method by proving that only a constant number of linearly independent bilinear optimality conditions exist for cones of positive polynomials, regardless of dimension.
In the second part we look at optimization with second order stochastic dominance constraints. Here the functional inequalities appear naturally, featuring the integral of the distribution function of a random variable defined by the decision variables. We develop new duality results as well as cutting plane methods that
are shown to perform well on a class of portfolio optimization problems. Finally we point out an interesting connection, arising as part of our duality considerations, between the theory of measures with given marginals and network feasibility. This results in a new proof of Strassen's Theorem from its trivial discrete case.
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electronic resource
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viii, 97 p. : ill.
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Ph.D.
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Includes bibliographical references (p. 92-96)
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by Gábor Rudolf
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Rudolf
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Gábor
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1979-
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Gábor Rudolf
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Alizadeh
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Farid Alizadeh
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Prekopa
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Andras
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Andras Prekopa
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Ruszczynski
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Andrzej
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Andrzej Ruszczynski
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Boros
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Endre
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Endre Boros
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Dentcheva
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Darinka
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Darinka Dentcheva
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Rutgers University
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Graduate School - New Brunswick
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2009
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2009-10
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xx
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Rutgers University Electronic Theses and Dissertations
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ETD
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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doi:10.7282/T3QF8T1H
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ETD doctoral
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Open
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Rudolf
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Gábor Rudolf
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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