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Books on the topic 'Convex duality theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

service), SpringerLink (Online, ed. Conjugate Duality in Convex Optimization. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2010.

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2

Duality in nonconvex approximation and optimization. New York: Springer, 2005.

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3

Șandru, Ovidiu-Ilie. Noneuclidean convexity: Applications in the programming theory. București: Editura Tehnică, 1998.

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4

Gao, David Yang. Duality principles in nonconvex systems: Theory, methods, and applications. Dordrecht: Kluwer Academic Publishers, 2000.

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5

Guédon, Olivier. Analytical and probabilistic methods in the geometry of convex bodies. Warszawa: Institute of Mathematics, Polish Academy of Sciences, 2014.

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6

1929-, Ponstein Jacob, ed. Convexity and duality in optimization: Proceedings of the Symposium on Convexity and Duality in Optimization held at the University of Groningen, the Netherlands, June 22, 1984. Berlin: Springer-Verlag, 1985.

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7

Nonsmooth mechanics and convex optimization. Boca Raton, FL: CRC Press/Taylor & Francis, 2011.

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8

Drigojias, Ioannis. Approximationseigenschaft und Dualität von gewichteten H⁽p̳⁾- Räumen. [Münster]: Drucktechnische Zentralstelle der Universität Münster, 1993.

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9

Singer, Ivan. Duality for Nonconvex Approximation and Optimization (CMS Books in Mathematics). Springer, 2006.

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10

Grad, Sorin-Mihai. Vector Optimization and Monotone Operators via Convex Duality: Recent Advances. Springer, 2016.

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11

Csetnek, Ernö Robert. Overcoming the failure of the classical generalized interior-point regularity conditions in convex optimization. Applications of the duality theory to enlargements of maximal monotone operators. Logos Verlag, 2010.

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12

Chambers, Robert G. Competitive Agents in Certain and Uncertain Markets. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780190063016.001.0001.

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This book uses concepts from optimization theory to develop an integrated analytic framework for treating consumer, producer, and market equilibrium analyses as special cases of a generic optimization problem. The same framework applies to both stochastic and non-stochastic decision settings, so that the latter is recognized as an (important) special case of the former. The analytic techniques are borrowed from convex analysis and variational analysis. Special emphasis is given to generalized notions of differentiability, conjugacy theory, and Fenchel's Duality Theorem. The book shows how virtually identical conjugate analyses form the basis for modeling economic behavior in each of the areas studied. The basic analytic concepts are borrowed from convex analysis. Special emphasis is given to generalized notions of differentiability, conjugacy theory, and Fenchel's Duality Theorem. It is demonstrated how virtually identical conjugate analyses form the basis for modelling economic behaviour in each of the areas studied.

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13

Network Flows and Monotropic Optimization. Athena Scientific, 1998.

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14

Bova, Paul M., and Paul M. Livingston. Univocity, Duality, and Ideal Genesis: Deleuze and Plato. Edinburgh University Press, 2018. http://dx.doi.org/10.3366/edinburgh/9781474412094.003.0005.

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John Bova and Paul M. Livingston’s “Univocity, Duality, and Ideal Genesis: Deleuze and Plato” elaborates an unorthodox yet powerful dualism in the writings of Plato. This dualism accounts for the structural origin of both supersensible ideas and the sensible particulars which participate in them. Further, this duality extends to the reflexive level of theory itself, recognizable in the incompatible metalogical demands for consistency and completeness. Bova and Livingston connect this formal dualism to Deleuze’s discussions of ideal genesis and the paradoxes of becoming. They show a presence of a proper “Platonism” of the Idea in Deleuze, and establish thereby the potential for a recuperation of Platonic dualism in the context of the Deleuzian univocity of being.

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15

Cones and Duality (Graduate Studies in Mathematics). American Mathematical Society, 2007.

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16

Caramello, Olivia. Theories, Sites, Toposes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.001.0001.

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This book is devoted to a general study of geometric theories from a topos-theoretic perspective. After recalling the necessary topos-theoretic preliminaries, it presents the main methodology it uses to extract ‘concrete’ information on theories from properties of their classifying toposes—the ‘bridge’ technique. As a first implementation of this methodology, a duality is established between the subtoposes of the classifying topos of a geometric theory and the geometric theory extensions (also called ‘quotients’) of the theory. Many concepts of elementary topos theory which apply to the lattice of subtoposes of a given topos are then transferred via this duality into the context of geometric theories. A second very general implementation of the ‘bridge’ technique is the investigation of the class of theories of presheaf type (i.e. classified by a presheaf topos). After establishing a number of preliminary results on flat functors in relation to classifying toposes, the book carries out a systematic investigation of this class resulting in a number of general results and a characterization theorem allowing one to test whether a given theory is of presheaf type by considering its models in arbitrary Grothendieck toposes. Expansions of geometric theories and faithful interpretations of theories of presheaf type are also investigated. As geometric theories can always be written (in many ways) as quotients of presheaf type theories, the study of quotients of a given theory of presheaf type is undertaken. Lastly, the book presents a number of applications in different fields of mathematics of the theory it develops.

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17

Caramello, Olivia. Lattices of theories. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0006.

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In this chapter, by using the duality theorem established in Chapter 3, many ideas and concepts of elementary topos theory are transferred into the context of geometric logic; these notions notably include the coHeyting algebra structure on the lattice of subtoposes of a given topos, open, closed, quasi-closed subtoposes, the dense-closed factorization of a geometric inclusion, coherent subtoposes, subtoposes with enough points, the surjection-inclusion factorization of a geometric morphism, skeletal inclusions, atoms in the lattice of subtoposes of a given topos, the Booleanization and DeMorganization of a topos. An explicit description of the Heyting operation between Grothendieck topologies on a given category and of the Grothendieck topology generated by a given collection of sieves is also obtained, as well as a number of results about the problem of ‘relativizing’ a local operator with respect to a given subtopos.

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18

Gragl, Paul. Introduction. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198796268.003.0001.

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This introductory chapter first presents the research question of this book, namely whether there is only one ‘law’. Subsequently, it situates this question in the context of normative conflicts between different bodies of law, which represent the fertile ground for theories such as monism, dualism, or pluralism. After briefly presenting these theories and their main characteristics, this chapter highlights various important arguments against monism, which have led to the (premature) conclusion that legal monism is already dead. This chapter concludes that the contrary is the case and concisely shows, by introducing the substantial chapters of this book, that there are many and convincing arguments for the continuing relevance of legal monism.

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19

Lee, Alexander. An Elective Empire. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199675159.003.0008.

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This chapter explores how the humanists’ dualism affected their understanding of the Empire’s constitutional disposition. Setting the humanists’ views in the context of contemporary struggles over the sources and nature of the emperor’s authority, it will demonstrate that—despite a flirtation with Roman popular sovereignty on at least two separate occasions, and a residual uncertainty about the significance of papal coronations—they were broadly willing to view the electoral college as the ultimate source of imperial authority. But though they followed—and sometimes even anticipated—their coevals’ political thought in some respects, it is striking that the humanists never sought to justify their understanding of the electoral college’s role in terms comparable to those used either in developing wider theories of political representation, or in defending communal government.

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20

Al-Rasheed, Madawi. The Son King. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780197558140.001.0001.

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The murder of journalist Jamal Khashoggi at the Saudi consulate in Istanbul by regime operatives shocked the international community and tarnished the reputation of the young, reformist Crown Prince Muhammad bin Salman. This book situates the murder in the context of the duality of reform and repression and challenges common wisdom about the inevitability of the latter. The author dismisses defunct views about the inescapable ‘Oriental Despotism’ as the only pathway to genuine reform in the country. Focusing on the prince’s divisive domestic, social and economic reforms, the author argues that the current wave of unprecedented repression is a function of the prince consolidating his power outside of the traditional consensus of royal family members and influential Saudi groups. But the divisive populist nationalism bin Salman has adopted, together with repressing the diverse critical voices of religious scholars, feminists and professionals, has failed to silence a vibrant young Saudi society and an articulate and connected youth cohort. Due to its repression, Saudi Arabia is now producing asylum seekers and refugees who seek safe havens abroad to pursue their quest for freedom, equality and dignity. While the regime continues to pursue them abroad and punish their families at home, exiled activists are determined to continue the struggle against one of the most repressive monarchies in the Arab world.

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21

Hamou, Philippe. Locke and Descartes on Selves and Thinking Substances. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198815037.003.0008.

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Locke’s construal of selves, persons, and thinking substances is notoriously difficult and the subject of wide controversy. In this chapter, it is suggested that we could go some way towards clarifying it by seeing it in the context of Descartes’s construal of the same or similar issues. The chapter argues that there are both strong threads of continuity (which may appear even stronger in the light of the recent reappraisal of Descartes’s so-called dualism) and a quite obvious (but often neglected) anti-Cartesian strand in Locke’s doctrine of the self. The target is to assess precisely where and why Locke departs from Descartes. The chapter shows, contrary to a common but misconceived view of Locke’s aim in Essay II. xvii, that it is not so much the Cartesian ‘substantiation’ of the self that Locke is arguing against, but rather its disembodiment.

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22

Lieu, Judith M., and Martinus C. de Boer, eds. The Oxford Handbook of Johannine Studies. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198739982.001.0001.

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The Oxford Handbook of Johannine Studies offers a comprehensive introduction to and discussion of contemporary study of the Gospel and Letters of John. The 24 chapters, all written by leading specialists in the field, cover the text and literary sources of the Johannine literature; its historical origins and context; and its conceptual background in Greek and Jewish thought, as well as its relationship to and reception among the Gnostics. Separate chapters discuss recent approaches to the Gospel and Letters from narrative, gender-related, ideological, and sociological perspectives, as well as their use of symbolism. The major Johannine theological themes are all discussed, including the role of ‘the Jews’, the attitude to Scripture and law, dualism, eschatology, the person and purpose of Jesus, the experience of eternal life and the Spirit, and ethics. The place of the Johannine literature in the church’s canon and the emergence of a commentary tradition close the volume. Each chapter gives a balanced overview of scholarly debate, while also offering a clearly presented response from the perspective of the author.

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